Problem: Solve the following equation for the variable u: 122 = 92 + 28 * u

Claude-3 Opus:

To solve the equation 122 = 92 + 28 * u for the variable u, we need to isolate u on one side of the equation. We can do this by subtracting 92 from both sides of the equation and then dividing both sides by 28.

Step 1: Subtract 92 from both sides of the equation.
122 - 92 = 92 - 92 + 28 * u
30 = 28 * u

Step 2: Divide both sides of the equation by 28.
30 ÷ 28 = 28 * u ÷ 28
30/28 = u
<<30/28=1.0714285714285714>>1.0714285714285714 = u

Therefore, the solution to the equation 122 = 92 + 28 * u is:
### Answer: u = 1.0714285714285714

Expected answer: 15/14

Correct? Yes

Problem: Solve the following equation for i: 42 = ((35 * i) - 34)

Claude-3 Opus:

To solve the equation 42 = ((35 * i) - 34) for i, we need to isolate the variable i on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
42 = ((35 * i) - 34)

Step 1: Add 34 to both sides of the equation to isolate the term containing i.
42 + 34 = ((35 * i) - 34) + 34
76 = 35 * i

Step 2: Divide both sides of the equation by 35 to solve for i.
76 ÷ 35 = (35 * i) ÷ 35
76/35 = i

Now, simplify the fraction 76/35:
76 ÷ 35 = 2.171428571...
This can be rounded to 2.17 (rounded to 2 decimal places).

### Answer: i ≈ 2.17

Expected answer: 76/35

Correct? No

Problem: Solve the following equation to find the value of r: 94 = 41 + 6 * r

Claude-3 Opus:

To solve for r, we need to isolate the variable on one side of the equation. We can do this by subtracting 41 from both sides of the equation and then dividing both sides by 6.

Given equation: 94 = 41 + 6 * r

Step 1: Subtract 41 from both sides of the equation.
94 - 41 = 41 - 41 + 6 * r
53 = 6 * r

Step 2: Divide both sides of the equation by 6.
53 ÷ 6 = (6 * r) ÷ 6
53 ÷ 6 = r
8.8333... = r

Therefore, the value of r is approximately 8.8333 (rounded to 4 decimal places).

### Answer: 8.8333

Expected answer: 53/6

Correct? No

Problem: Determine the value of "i" from the following equation: 158 = ((19 * i) + 94)

Claude-3 Opus:

To solve for the value of "i", let's use the following steps:

1. Subtract 94 from both sides of the equation to isolate the term containing "i":
158 - 94 = ((19 * i) + 94) - 94
64 = 19 * i

2. Divide both sides of the equation by 19 to solve for "i":
64 ÷ 19 = (19 * i) ÷ 19
<<64/19=3.368421052631579>>3.368421052631579 = i

Therefore, the value of "i" is approximately 3.368421052631579.

### Answer: 3.368421052631579

Expected answer: 64/19

Correct? No

Problem: Solve the following equation for 'q': 134 = ((30 * q) + 54)

Claude-3 Opus:

To solve the equation 134 = ((30 * q) + 54) for 'q', we need to isolate 'q' on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Step 1: Subtract 54 from both sides of the equation to isolate the term containing 'q'.
134 - 54 = ((30 * q) + 54) - 54
80 = 30 * q

Step 2: Divide both sides of the equation by 30 to solve for 'q'.
80 ÷ 30 = (30 * q) ÷ 30
80/30 = q
<<80/30=round(2.6666666666666665, 2)>>2.67 = q

Therefore, the solution to the equation 134 = ((30 * q) + 54) is q = 2.67.

### Answer: 2.67

Expected answer: 8/3

Correct? No

Problem: Solve the following linear equation to find the value of y: 94 = (27 + y)

Claude-3 Opus:

To solve the linear equation 94 = (27 + y) for y, we need to isolate y on one side of the equation.

Given:
94 = (27 + y)

Step 1: Subtract 27 from both sides of the equation to isolate y.
94 - 27 = (27 + y) - 27
67 = y

Therefore, the value of y is 67.

### Answer: y = 67

Expected answer: 67

Correct? Yes

Problem: Solve the following linear equation for the value of h: 9 = ((23 * h) - 70)

Claude-3 Opus:

To solve the linear equation 9 = ((23 * h) - 70) for the value of h, we need to isolate the variable h on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
9 = ((23 * h) - 70)

Step 1: Add 70 to both sides of the equation to isolate the term containing h.
9 + 70 = ((23 * h) - 70) + 70
79 = 23 * h

Step 2: Divide both sides of the equation by 23 to solve for h.
79 ÷ 23 = (23 * h) ÷ 23
79 ÷ 23 = h

Now, we can calculate the value of h:
h = 79 ÷ 23
h = 3.434782608695652 (rounded to 15 decimal places)

### Answer: 3.434782608695652

Expected answer: 79/23

Correct? No

Problem: Solve the following equation to find the value of t: 92 = 33 * t + 26

Claude-3 Opus:

To solve for t in the equation 92 = 33 * t + 26, we need to isolate the variable t on one side of the equation. We can do this by subtracting 26 from both sides of the equation to eliminate the constant term on the right side. Then, we'll divide both sides by 33 to solve for t.

Step 1: Subtract 26 from both sides of the equation.
92 - 26 = 33 * t + 26 - 26
66 = 33 * t

Step 2: Divide both sides of the equation by 33.
66 ÷ 33 = 33 * t ÷ 33
2 = t

Therefore, the value of t that satisfies the equation 92 = 33 * t + 26 is 2.

### Answer: 2

Expected answer: 2

Correct? Yes

Problem: Solve the following linear equation to find the value of e: 123 = ((15 * e) + 29).

Claude-3 Opus:

To solve the linear equation 123 = ((15 * e) + 29) for the value of e, we need to isolate the variable e on one side of the equation.

Step 1: Subtract 29 from both sides of the equation to isolate the term containing e.
123 - 29 = ((15 * e) + 29) - 29
94 = 15 * e

Step 2: Divide both sides of the equation by 15 to solve for e.
94 ÷ 15 = (15 * e) ÷ 15
<<94/15=6.266666666666667>>6.266666666666667 = e

Therefore, the value of e that satisfies the equation 123 = ((15 * e) + 29) is approximately 6.266666666666667.

### Answer: 6.266666666666667

Expected answer: 94/15

Correct? Yes

Problem: Solve the following equation to find the value of 'k': 16 = ((75 * k) - 80)

Claude-3 Opus:

To solve the equation 16 = ((75 * k) - 80) for the value of 'k', we need to isolate 'k' on one side of the equation.

Step 1: Add 80 to both sides of the equation to isolate the term containing 'k'.
16 + 80 = ((75 * k) - 80) + 80
96 = 75 * k

Step 2: Divide both sides of the equation by 75 to solve for 'k'.
96 ÷ 75 = (75 * k) ÷ 75
<<96/75=1.28>>1.28 = k

Therefore, the value of 'k' is 1.28.

### Answer: 1.28

Expected answer: 32/25

Correct? Yes

Problem: Solve for q in the following equation: 131 = ((5 * q) + 89)

Claude-3 Opus:

To solve for q in the equation 131 = ((5 * q) + 89), we need to isolate the variable q on one side of the equation. We can do this by using inverse operations to undo the operations applied to q.

Given:
131 = ((5 * q) + 89)

Step 1: Subtract 89 from both sides of the equation to isolate the term containing q.
131 - 89 = ((5 * q) + 89) - 89
42 = 5 * q

Step 2: Divide both sides of the equation by 5 to solve for q.
42 ÷ 5 = (5 * q) ÷ 5
8.4 = q

Therefore, the value of q that satisfies the equation 131 = ((5 * q) + 89) is 8.4.

### Answer: 8.4

Expected answer: 42/5

Correct? Yes

Problem: Find the value of p that satisfies the following equation: 147 = ((38 * p) + 56)

Claude-3 Opus:

To find the value of p, we need to solve the equation 147 = ((38 * p) + 56) for p.

Step 1: Subtract 56 from both sides of the equation to isolate the term containing p.
147 - 56 = ((38 * p) + 56) - 56
91 = 38 * p

Step 2: Divide both sides of the equation by 38 to solve for p.
91 ÷ 38 = (38 * p) ÷ 38
91 ÷ 38 = p
<<91/38=2.3947368421052633>>2.3947368421052633 = p

Therefore, the value of p that satisfies the equation 147 = ((38 * p) + 56) is approximately 2.3947368421052633.

### Answer: 2.3947368421052633

Expected answer: 91/38

Correct? Yes

Problem: Solve the following equation to find the value of 'j': 76 = 42 * j + 23

Claude-3 Opus:

To solve for 'j', we need to isolate the variable on one side of the equation. We can do this by subtracting 23 from both sides of the equation to eliminate the constant term on the right side:

76 = 42 * j + 23
76 - 23 = 42 * j + 23 - 23
53 = 42 * j

Now, we can divide both sides of the equation by 42 to isolate 'j':

53 = 42 * j
53 / 42 = 42 * j / 42
53 / 42 = j

Simplifying the fraction:
53 / 42 = 1.2619047619047619

Therefore, the value of 'j' is approximately 1.26.

### Answer: 1.26

Expected answer: 53/42

Correct? No

Problem: Solve the following equation to find the value of 'l': 138 = 43 + 25 * l

Claude-3 Opus:

To solve for 'l', we need to isolate the variable on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given equation: 138 = 43 + 25 * l

Step 1: Subtract 43 from both sides of the equation to isolate the term containing 'l'.
138 - 43 = 43 - 43 + 25 * l
95 = 25 * l

Step 2: Divide both sides of the equation by 25 to solve for 'l'.
95 ÷ 25 = (25 * l) ÷ 25
95 ÷ 25 = l
3.8 = l

Therefore, the value of 'l' is 3.8.

### Answer: 3.8

Expected answer: 19/5

Correct? Yes

Problem: Solve the following equation to find the unknown w: 80 = ((24 * w) + 35)

Claude-3 Opus:

To solve the equation 80 = ((24 * w) + 35) for the unknown w, we need to isolate w on one side of the equation. We can do this by subtracting 35 from both sides of the equation and then dividing both sides by 24.

Step 1: Subtract 35 from both sides of the equation.
80 - 35 = ((24 * w) + 35) - 35
45 = 24 * w

Step 2: Divide both sides of the equation by 24.
45 ÷ 24 = (24 * w) ÷ 24
<<45/24=1.875>>1.875 = w

Therefore, the value of w that satisfies the equation 80 = ((24 * w) + 35) is 1.875.

### Answer: 1.875

Expected answer: 15/8

Correct? Yes

Problem: Solve the following linear equation to find the value of x: 77 = (33 + (14 * x))

Claude-3 Opus:

To solve the linear equation 77 = (33 + (14 * x)), we need to isolate the variable x on one side of the equation.

Step 1: Simplify the right side of the equation by removing the parentheses.
77 = 33 + 14x

Step 2: Subtract 33 from both sides of the equation to isolate the term containing x.
77 - 33 = 33 - 33 + 14x
44 = 14x

Step 3: Divide both sides of the equation by 14 to solve for x.
44 ÷ 14 = 14x ÷ 14
x = 44 ÷ 14
x = 3.142857...

Since the question asks for the value of x, we can round the answer to a reasonable number of decimal places, such as 3.14 or 3.143.

### Answer: 3.143

Expected answer: 22/7

Correct? No

Problem: Solve the following linear equation to find the value of y: 110 = 12 + 88 * y

Claude-3 Opus:

To solve the linear equation 110 = 12 + 88 * y for y, we need to isolate y on one side of the equation.

Step 1: Subtract 12 from both sides of the equation to isolate the term containing y.
110 - 12 = 12 - 12 + 88 * y
98 = 88 * y

Step 2: Divide both sides of the equation by 88 to solve for y.
98 ÷ 88 = 88 * y ÷ 88
<<98/88=49/44>>49/44 = y

Therefore, the value of y that satisfies the equation 110 = 12 + 88 * y is 49/44.

### Answer: 49/44

Expected answer: 49/44

Correct? Yes

Problem: Solve the following linear equation for the variable 's': 179 = 82 * s + 80

Claude-3 Opus:

To solve the linear equation 179 = 82 * s + 80 for the variable 's', we need to isolate 's' on one side of the equation. We can do this by subtracting 80 from both sides of the equation to eliminate the constant term on the right side. Then, we'll divide both sides by 82 to isolate 's'.

Step 1: Subtract 80 from both sides of the equation.
179 - 80 = 82 * s + 80 - 80
99 = 82 * s

Step 2: Divide both sides of the equation by 82.
99 ÷ 82 = 82 * s ÷ 82
99 ÷ 82 = s
<<99/82=1.207317073170732>>1.207317073170732 = s

Therefore, the solution to the linear equation 179 = 82 * s + 80 is:
### Answer: s = 1.207317073170732

Expected answer: 99/82

Correct? No

Problem: Solve the following equation for m: 129 = 26 * m + 66

Claude-3 Opus:

To solve the equation 129 = 26 * m + 66 for m, we need to isolate the variable m on one side of the equation. We can do this by subtracting 66 from both sides of the equation to eliminate the constant term on the right side.

129 - 66 = 26 * m + 66 - 66
63 = 26 * m

Now, we can divide both sides of the equation by 26 to isolate m.

63 ÷ 26 = 26 * m ÷ 26
63/26 = m
<<63/26=2.423076923076923>> 

Therefore, the solution to the equation 129 = 26 * m + 66 is:

### Answer: m = 63/26 (or approximately 2.423076923076923)

Expected answer: 63/26

Correct? Yes

Problem: Solve the following linear equation for q: 82 = ((27 * q) - 17)

Claude-3 Opus:

To solve the linear equation 82 = ((27 * q) - 17) for q, we need to isolate q on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Given:
82 = ((27 * q) - 17)

Step 1: Add 17 to both sides of the equation to isolate the term containing q.
82 + 17 = ((27 * q) - 17) + 17
99 = 27 * q

Step 2: Divide both sides of the equation by 27 to solve for q.
99 ÷ 27 = (27 * q) ÷ 27
99/27 = q
<<99/27=3.6666666666666665>>

Therefore, the solution to the linear equation 82 = ((27 * q) - 17) is q = 99/27.

### Answer: 99/27 or approximately 3.67

Expected answer: 11/3

Correct? Yes

Problem: Solve the following linear equation for the variable k: 141 = (64 + (22 * k))

Claude-3 Opus:

To solve the linear equation 141 = (64 + (22 * k)) for the variable k, we need to isolate k on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
141 = (64 + (22 * k))

Step 1: Simplify the right side of the equation by removing the parentheses.
141 = 64 + 22k

Step 2: Subtract 64 from both sides of the equation to isolate the term containing k.
141 - 64 = 64 - 64 + 22k
77 = 22k

Step 3: Divide both sides of the equation by 22 to solve for k.
77 ÷ 22 = 22k ÷ 22
<<77/22=3.5>>3.5 = k

Therefore, the solution to the linear equation 141 = (64 + (22 * k)) is k = 3.5.

### Answer: 3.5

Expected answer: 7/2

Correct? Yes

Problem: Determine the value of 'v' by solving this linear equation: 175 = 91 + 45 * v

Claude-3 Opus:

To solve for 'v' in the linear equation 175 = 91 + 45 * v, we need to isolate the variable 'v' on one side of the equation.

Step 1: Subtract 91 from both sides of the equation to isolate the term containing 'v'.
175 - 91 = 91 - 91 + 45 * v
84 = 45 * v

Step 2: Divide both sides of the equation by 45 to solve for 'v'.
84 ÷ 45 = (45 * v) ÷ 45
84 ÷ 45 = v
<<84/45=1.8666666666666667>>1.866667 = v (rounded to 6 decimal places)

Therefore, the value of 'v' in the linear equation 175 = 91 + 45 * v is approximately 1.866667.

### Answer: 1.866667

Expected answer: 28/15

Correct? No

Problem: Solve the following equation for the value of k: 50 = ((63 * k) - 18)

Claude-3 Opus:

To solve the equation 50 = ((63 * k) - 18) for the value of k, we need to isolate k on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
50 = ((63 * k) - 18)

Step 1: Add 18 to both sides of the equation to isolate the term containing k.
50 + 18 = ((63 * k) - 18) + 18
68 = 63 * k

Step 2: Divide both sides of the equation by 63 to solve for k.
68 ÷ 63 = (63 * k) ÷ 63
68 ÷ 63 = k
<<68/63=1.0793650793650793>>1.0793650793650793 = k

Therefore, the value of k that satisfies the equation 50 = ((63 * k) - 18) is approximately 1.0793650793650793.

### Answer: 1.0793650793650793

Expected answer: 68/63

Correct? Yes

Problem: Solve the following equation for l: 65 = ((8 * l) - 10)

Claude-3 Opus:

To solve the equation 65 = ((8 * l) - 10) for l, we need to isolate the variable l on one side of the equation. We can do this by using inverse operations to undo the operations performed on l.

Given:
65 = ((8 * l) - 10)

Step 1: Add 10 to both sides of the equation to isolate the term containing l.
65 + 10 = ((8 * l) - 10) + 10
75 = (8 * l)

Step 2: Divide both sides of the equation by 8 to solve for l.
75 ÷ 8 = (8 * l) ÷ 8
9.375 = l

Therefore, the solution to the equation 65 = ((8 * l) - 10) is l = 9.375.

### Answer: 9.375

Expected answer: 75/8

Correct? Yes

Problem: Solve the following equation: 5 = ((10 * u) - 34)

Claude-3 Opus:

To solve the equation 5 = ((10 * u) - 34), we need to isolate the variable u on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
5 = ((10 * u) - 34)

Step 1: Add 34 to both sides of the equation to isolate the term containing u.
5 + 34 = ((10 * u) - 34) + 34
39 = 10 * u

Step 2: Divide both sides of the equation by 10 to solve for u.
39 ÷ 10 = (10 * u) ÷ 10
3.9 = u

Therefore, the solution to the equation 5 = ((10 * u) - 34) is u = 3.9.

### Answer: 3.9

Expected answer: 39/10

Correct? Yes

Problem: Solve the following problem in linear equations for variable 'a': 91 = 9 * a + 61

Claude-3 Opus:

To solve the linear equation 91 = 9 * a + 61 for the variable 'a', we need to isolate 'a' on one side of the equation. We can do this by subtracting 61 from both sides of the equation to eliminate the constant term on the right-hand side.

Step 1: Subtract 61 from both sides of the equation.
91 - 61 = 9 * a + 61 - 61
30 = 9 * a

Step 2: Divide both sides of the equation by 9 to isolate 'a'.
30 ÷ 9 = 9 * a ÷ 9
<<30/9=3.33333333333333>>3.33333333333333 = a

Therefore, the solution to the linear equation 91 = 9 * a + 61 is:
### Answer: a = 3.33333333333333

Expected answer: 10/3

Correct? No

Problem: Solve the following linear equation for the variable i: 157 = 53 * i + 61

Claude-3 Opus:

To solve the linear equation 157 = 53 * i + 61 for the variable i, we need to isolate i on one side of the equation. We can do this by subtracting 61 from both sides of the equation to eliminate the constant term on the right side, and then dividing both sides by 53.

Step 1: Subtract 61 from both sides of the equation.
157 - 61 = 53 * i + 61 - 61
96 = 53 * i

Step 2: Divide both sides of the equation by 53.
96 ÷ 53 = 53 * i ÷ 53
96/53 = i
<<96/53=1.8113207547169812>>1.8113207547169812 = i

Therefore, the solution to the linear equation 157 = 53 * i + 61 is:
### Answer: i = 1.8113207547169812

Expected answer: 96/53

Correct? Yes

Problem: Solve the following linear equation for the value of q: 71 = ((24 * q) + 14)

Claude-3 Opus:

To solve the linear equation 71 = ((24 * q) + 14) for the value of q, we need to isolate q on one side of the equation. We can do this by subtracting 14 from both sides of the equation and then dividing both sides by 24.

Step 1: Subtract 14 from both sides of the equation.
71 - 14 = ((24 * q) + 14) - 14
57 = 24 * q

Step 2: Divide both sides of the equation by 24.
57 ÷ 24 = (24 * q) ÷ 24
<<57/24=2.375>>2.375 = q

Therefore, the value of q that satisfies the equation 71 = ((24 * q) + 14) is 2.375.

### Answer: 2.375

Expected answer: 19/8

Correct? Yes

Problem: Solve the following linear equation for the value of i: 163 = 96 + 14 * i

Claude-3 Opus:

To solve the linear equation 163 = 96 + 14 * i for the value of i, we need to isolate the variable i on one side of the equation.

Step 1: Subtract 96 from both sides of the equation to isolate the term containing i.
163 - 96 = 96 - 96 + 14 * i
67 = 14 * i

Step 2: Divide both sides of the equation by 14 to solve for i.
67 ÷ 14 = (14 * i) ÷ 14
67 ÷ 14 = i
i = 67 ÷ 14
i = 4.785714285714286

Therefore, the value of i that satisfies the equation 163 = 96 + 14 * i is:

### Answer: 4.785714285714286

Expected answer: 67/14

Correct? Yes

Problem: Solve the following linear equation for the value of e: 59 = (70 * e) - 23

Claude-3 Opus:

To solve the linear equation 59 = (70 * e) - 23 for the value of e, we need to isolate the variable e on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Given:
59 = (70 * e) - 23

Step 1: Add 23 to both sides of the equation to isolate the term containing e on the right-hand side.
59 + 23 = (70 * e) - 23 + 23
82 = 70 * e

Step 2: Divide both sides of the equation by 70 to solve for e.
82 ÷ 70 = (70 * e) ÷ 70
82/70 = e
<<82/70=1.1714285714285714>>1.1714285714285714 = e

Therefore, the value of e that satisfies the equation 59 = (70 * e) - 23 is approximately 1.1714285714285714.

### Answer: 1.1714285714285714

Expected answer: 41/35

Correct? Yes

Problem: Solve the following linear equation for o: 147 = 36 * o + 74

Claude-3 Opus:

To solve the linear equation 147 = 36 * o + 74 for o, we need to isolate the variable o on one side of the equation. We can do this by subtracting 74 from both sides of the equation and then dividing both sides by 36.

Step 1: Subtract 74 from both sides of the equation.
147 - 74 = 36 * o + 74 - 74
73 = 36 * o

Step 2: Divide both sides of the equation by 36.
73 ÷ 36 = 36 * o ÷ 36
73 ÷ 36 = o

Now, we need to perform the division 73 ÷ 36.
73 ÷ 36 = 2 remainder 1
1 ÷ 36 = 1/36

Therefore, 73 ÷ 36 = 2 + 1/36 = 2 1/36 (or 2.027777... as a decimal).

### Answer: o = 2 1/36 (or 2.027777...)

Expected answer: 73/36

Correct? Yes

Problem: Solve the following equation: 71 = 93 - (13 * d)

Claude-3 Opus:

To solve the equation 71 = 93 - (13 * d), we need to isolate the variable d on one side of the equation.

Step 1: Simplify the right side of the equation by distributing the negative sign.
71 = 93 - 13d

Step 2: Subtract 93 from both sides of the equation to isolate the term containing d on the right side.
71 - 93 = 93 - 93 - 13d
-22 = -13d

Step 3: Divide both sides of the equation by -13 to solve for d.
-22 ÷ (-13) = -13d ÷ (-13)
<<-22/-13=1.6923076923076923>>1.6923076923076923 = d

Therefore, the solution to the equation 71 = 93 - (13 * d) is d = 1.6923076923076923.

### Answer: 1.6923076923076923

Expected answer: 22/13

Correct? Yes

Problem: Solve the following equation to find the value of n: 118 = 64 + 6 * n

Claude-3 Opus:

To solve for n in the equation 118 = 64 + 6 * n, we need to isolate the variable n on one side of the equation. We can do this by subtracting 64 from both sides of the equation and then dividing both sides by 6.

Step 1: Subtract 64 from both sides of the equation.
118 - 64 = 64 - 64 + 6 * n
54 = 6 * n

Step 2: Divide both sides of the equation by 6.
54 ÷ 6 = (6 * n) ÷ 6
9 = n

Therefore, the value of n that satisfies the equation 118 = 64 + 6 * n is 9.

### Answer: 9

Expected answer: 9

Correct? Yes

Problem: Solve the following equation to find the value of 'd': 61 = ((5 * d) - 7)

Claude-3 Opus:

To solve for 'd', we need to isolate the variable on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given equation: 61 = ((5 * d) - 7)

Step 1: Add 7 to both sides of the equation to isolate the term containing 'd'.
61 + 7 = ((5 * d) - 7) + 7
68 = (5 * d)

Step 2: Divide both sides of the equation by 5 to isolate 'd'.
68 ÷ 5 = (5 * d) ÷ 5
13.6 = d

Therefore, the value of 'd' is 13.6.

### Answer: 13.6

Expected answer: 68/5

Correct? Yes

Problem: Solve the following linear equation for the value of z: 79 = ((8 * z) - 18)

Claude-3 Opus:

To solve the linear equation 79 = ((8 * z) - 18) for the value of z, we need to isolate the variable z on one side of the equation. We can do this by using inverse operations to undo the operations performed on z.

Given:
79 = ((8 * z) - 18)

Step 1: Add 18 to both sides of the equation to isolate the term containing z.
79 + 18 = ((8 * z) - 18) + 18
97 = 8 * z

Step 2: Divide both sides of the equation by 8 to solve for z.
97 ÷ 8 = (8 * z) ÷ 8
97/8 = z
<<97/8=12.125>>12.125 = z

Therefore, the value of z that satisfies the equation 79 = ((8 * z) - 18) is 12.125.

### Answer: 12.125

Expected answer: 97/8

Correct? Yes

Problem: Solve the following linear equation for the value of z: 129 = ((2 * z) + 63)

Claude-3 Opus:

To solve the linear equation 129 = ((2 * z) + 63) for the value of z, we need to isolate the variable z on one side of the equation. We can do this by subtracting 63 from both sides of the equation and then dividing both sides by 2.

Step 1: Subtract 63 from both sides of the equation.
129 - 63 = ((2 * z) + 63) - 63
66 = 2 * z

Step 2: Divide both sides of the equation by 2.
66 ÷ 2 = (2 * z) ÷ 2
33 = z

Therefore, the value of z that satisfies the equation 129 = ((2 * z) + 63) is 33.

### Answer: 33

Expected answer: 33

Correct? Yes

Problem: Solve the following linear equation for e: 127 = (29 + (32 * e))

Claude-3 Opus:

To solve the linear equation 127 = (29 + (32 * e)) for e, we need to isolate the variable e on one side of the equation.

Step 1: Simplify the right side of the equation by removing the parentheses.
127 = 29 + 32e

Step 2: Subtract 29 from both sides of the equation to isolate the term containing e.
127 - 29 = 29 - 29 + 32e
98 = 32e

Step 3: Divide both sides of the equation by 32 to solve for e.
98 ÷ 32 = 32e ÷ 32
<<98/32=3.0625>>3.0625 = e

Therefore, the solution to the linear equation 127 = (29 + (32 * e)) is e = 3.0625.

### Answer: 3.0625

Expected answer: 49/16

Correct? Yes

Problem: Solve the following linear equation for the value of x: 30 = ((50 * x) - 35)

Claude-3 Opus:

To solve the linear equation 30 = ((50 * x) - 35) for x, we need to isolate the variable x on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Given:
30 = ((50 * x) - 35)

Step 1: Add 35 to both sides of the equation to isolate the term containing x.
30 + 35 = ((50 * x) - 35) + 35
65 = 50 * x

Step 2: Divide both sides of the equation by 50 to solve for x.
65 ÷ 50 = (50 * x) ÷ 50
1.3 = x

Therefore, the value of x that satisfies the equation 30 = ((50 * x) - 35) is 1.3.

### Answer: 1.3

Expected answer: 13/10

Correct? Yes

Problem: Solve the following equation for x: 66 = 9 + 10 * x

Claude-3 Opus:

To solve the equation 66 = 9 + 10 * x for x, we need to isolate the variable x on one side of the equation. We can do this by using inverse operations.

Given equation: 66 = 9 + 10 * x

Step 1: Subtract 9 from both sides of the equation to isolate the term containing x.
66 - 9 = 9 - 9 + 10 * x
57 = 10 * x

Step 2: Divide both sides of the equation by 10 to solve for x.
57 ÷ 10 = (10 * x) ÷ 10
5.7 = x

Therefore, the solution to the equation 66 = 9 + 10 * x is x = 5.7.

### Answer: 5.7

Expected answer: 57/10

Correct? Yes

Problem: Solve the following algebraic equation for the unknown variable a: 103 = ((38 * a) + 51)

Claude-3 Opus:

To solve the algebraic equation 103 = ((38 * a) + 51) for the unknown variable a, we need to isolate the variable on one side of the equation. We can do this by using inverse operations.

Given:
103 = ((38 * a) + 51)

Step 1: Subtract 51 from both sides of the equation to isolate the term containing the variable a.
103 - 51 = ((38 * a) + 51) - 51
52 = 38 * a

Step 2: Divide both sides of the equation by 38 to solve for a.
52 ÷ 38 = (38 * a) ÷ 38
<<52/38=1.368421052631579>>1.368421052631579 = a

Therefore, the solution to the equation 103 = ((38 * a) + 51) is:
### Answer: a = 1.368421052631579

Expected answer: 26/19

Correct? Yes

Problem: Determine the value of f in the following equation: 105 = 28 * f + 8

Claude-3 Opus:

To solve for f in the equation 105 = 28 * f + 8, we need to isolate the variable f on one side of the equation.

Step 1: Subtract 8 from both sides of the equation to isolate the term containing f.
105 - 8 = 28 * f + 8 - 8
97 = 28 * f

Step 2: Divide both sides of the equation by 28 to solve for f.
97 ÷ 28 = 28 * f ÷ 28
97 ÷ 28 = f
<<97/28=3.4642857142857144>>3.4642857142857144 = f

Therefore, the value of f in the equation 105 = 28 * f + 8 is 3.4642857142857144.

### Answer: 3.4642857142857144

Expected answer: 97/28

Correct? Yes

Problem: Solve the linear equation for u: 12 = 63 - 50 * u

Claude-3 Opus:

To solve the linear equation for u, we need to isolate the variable u on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Given equation: 12 = 63 - 50 * u

Step 1: Subtract 63 from both sides of the equation to isolate the term containing u.
12 - 63 = 63 - 50 * u - 63
-51 = -50 * u

Step 2: Divide both sides of the equation by -50 to isolate u.
-51 ÷ (-50) = -50 * u ÷ (-50)
51/50 = u

Therefore, the solution to the linear equation 12 = 63 - 50 * u is:
### Answer: u = 51/50 (or 1.02)

Expected answer: 51/50

Correct? Yes

Problem: Solve the following equation for the value of 'b': 60 = 42 + (10 * b)

Claude-3 Opus:

To solve the equation 60 = 42 + (10 * b) for the value of 'b', we need to isolate 'b' on one side of the equation.

Step 1: Subtract 42 from both sides of the equation to isolate the term containing 'b'.
60 - 42 = 42 - 42 + (10 * b)
18 = 10 * b

Step 2: Divide both sides of the equation by 10 to solve for 'b'.
18 ÷ 10 = (10 * b) ÷ 10
1.8 = b

Therefore, the value of 'b' is 1.8.

### Answer: 1.8

Expected answer: 9/5

Correct? Yes

Problem: Solve the following linear equation for the variable 'j': 84 = ((25 * j) + 13)

Claude-3 Opus:

To solve the linear equation 84 = ((25 * j) + 13) for the variable 'j', we need to isolate 'j' on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Step 1: Subtract 13 from both sides of the equation to isolate the term containing 'j'.
84 - 13 = ((25 * j) + 13) - 13
71 = 25 * j

Step 2: Divide both sides of the equation by 25 to solve for 'j'.
71 ÷ 25 = (25 * j) ÷ 25
71/25 = j

Therefore, the solution to the linear equation 84 = ((25 * j) + 13) is:
j = 71/25

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1.
j = 71/25

### Answer: j = 71/25

Expected answer: 71/25

Correct? Yes

Problem: Solve the following linear equation for s: 153 = 91 + 5 * s

Claude-3 Opus:

To solve the linear equation 153 = 91 + 5 * s for s, we need to isolate the variable s on one side of the equation. We can do this by subtracting 91 from both sides of the equation to eliminate the constant term on the right side.

153 - 91 = 91 - 91 + 5 * s
62 = 5 * s

Now, we can divide both sides of the equation by 5 to isolate s.

62 ÷ 5 = (5 * s) ÷ 5
<<62/5=12.4>>12.4 = s

Therefore, the solution to the linear equation 153 = 91 + 5 * s is s = 12.4.

### Answer: 12.4

Expected answer: 62/5

Correct? Yes

Problem: Solve for g in the following equation: 65 = (22 + (30 * g))

Claude-3 Opus:

To solve for g in the equation 65 = (22 + (30 * g)), we need to isolate the variable g on one side of the equation.

Step 1: Simplify the right side of the equation by removing the parentheses.
65 = 22 + 30g

Step 2: Subtract 22 from both sides of the equation to isolate the term containing g.
65 - 22 = 22 - 22 + 30g
43 = 30g

Step 3: Divide both sides of the equation by 30 to solve for g.
43 ÷ 30 = 30g ÷ 30
<<43/30=1.4333333333333333>>1.4333333333333333 = g

Therefore, the value of g that satisfies the equation 65 = (22 + (30 * g)) is approximately 1.4333333333333333.

### Answer: 1.4333333333333333

Expected answer: 43/30

Correct? Yes

Problem: Solve the following linear equation for the value of f: 96 = ((29 * f) + 10)

Claude-3 Opus:

To solve the linear equation 96 = ((29 * f) + 10) for the value of f, we need to isolate the variable f on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Step 1: Subtract 10 from both sides of the equation to isolate the term containing f.
96 - 10 = ((29 * f) + 10) - 10
86 = 29 * f

Step 2: Divide both sides of the equation by 29 to solve for f.
86 ÷ 29 = (29 * f) ÷ 29
86 ÷ 29 = f
<<86/29=2.9655172413793105>>2.9655172413793105 = f

Therefore, the value of f that satisfies the equation 96 = ((29 * f) + 10) is approximately 2.9655172413793105.

### Answer: 2.9655172413793105

Expected answer: 86/29

Correct? Yes

Problem: Solve the following equation for the variable q: 80 = (19 + (14 * q))

Claude-3 Opus:

To solve the equation 80 = (19 + (14 * q)) for the variable q, we need to isolate q on one side of the equation. We can do this by using inverse operations to undo the operations performed on q.

Given:
80 = (19 + (14 * q))

Step 1: Simplify the right side of the equation by removing the parentheses.
80 = 19 + 14q

Step 2: Subtract 19 from both sides of the equation to isolate the term containing q.
80 - 19 = 19 - 19 + 14q
61 = 14q

Step 3: Divide both sides of the equation by 14 to solve for q.
61 ÷ 14 = 14q ÷ 14
<<61/14=4.357142857142857>>4.357142857142857 = q

Therefore, the solution to the equation 80 = (19 + (14 * q)) is:
### Answer: q = 4.357142857142857

Expected answer: 61/14

Correct? Yes

Problem: Solve the following linear equation for the variable 'm': 145 = 95 + 46 * m

Claude-3 Opus:

To solve the linear equation 145 = 95 + 46 * m for the variable 'm', we need to isolate 'm' on one side of the equation. We can do this by subtracting 95 from both sides of the equation and then dividing both sides by 46.

Step 1: Subtract 95 from both sides of the equation.
145 - 95 = 95 - 95 + 46 * m
50 = 46 * m

Step 2: Divide both sides of the equation by 46.
50 ÷ 46 = (46 * m) ÷ 46
50 ÷ 46 = m
<<50/46=1.0869565217391304>>1.0869565217391304 = m

Therefore, the solution to the linear equation 145 = 95 + 46 * m is:
### Answer: m = 1.0869565217391304

Expected answer: 25/23

Correct? Yes

Problem: Solve the following equation for the value of 'i': 68 = 13 + 6 * i

Claude-3 Opus:

To solve the equation 68 = 13 + 6 * i for the value of 'i', we need to isolate 'i' on one side of the equation.

Step 1: Subtract 13 from both sides of the equation to isolate the term containing 'i' on the right-hand side.
68 - 13 = 13 - 13 + 6 * i
55 = 6 * i

Step 2: Divide both sides of the equation by 6 to solve for 'i'.
55 ÷ 6 = (6 * i) ÷ 6
55 ÷ 6 = i
<<55/6=9.166666666666666>>9.166666666666666 = i

Therefore, the value of 'i' in the equation 68 = 13 + 6 * i is approximately 9.166666666666666.

### Answer: 9.166666666666666

Expected answer: 55/6

Correct? Yes

Problem: Solve the following equation for the value of h: 25 = ((74 * h) - 61)

Claude-3 Opus:

To solve the equation 25 = ((74 * h) - 61) for h, we need to isolate the variable h on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
25 = ((74 * h) - 61)

Step 1: Add 61 to both sides of the equation to isolate the term containing h.
25 + 61 = ((74 * h) - 61) + 61
86 = 74 * h

Step 2: Divide both sides of the equation by 74 to solve for h.
86 ÷ 74 = (74 * h) ÷ 74
86/74 = h

Now, simplify the fraction:
86 ÷ 74 = 1.162162162...
We can round this to three decimal places.

### Answer: 1.162

Expected answer: 43/37

Correct? No

Problem: Solve the following linear equation for the value of q: 51 = ((6 * q) - 30)

Claude-3 Opus:

To solve the linear equation 51 = ((6 * q) - 30) for the value of q, we need to isolate q on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
51 = ((6 * q) - 30)

Step 1: Add 30 to both sides of the equation to isolate the term containing q.
51 + 30 = ((6 * q) - 30) + 30
81 = 6 * q

Step 2: Divide both sides of the equation by 6 to solve for q.
81 ÷ 6 = (6 * q) ÷ 6
13.5 = q

Therefore, the value of q that satisfies the equation 51 = ((6 * q) - 30) is 13.5.

### Answer: 13.5

Expected answer: 27/2

Correct? Yes

Problem: Find the value of r in the following linear equation: 38 = 81 - 36 * r

Claude-3 Opus:

To find the value of r, we need to solve the linear equation 38 = 81 - 36 * r for r.

Step 1: Subtract 81 from both sides of the equation.
38 - 81 = 81 - 81 - 36 * r
-43 = -36 * r

Step 2: Divide both sides of the equation by -36.
-43 ÷ (-36) = -36 * r ÷ (-36)
<<-43/-36=1.1944444444444444>>1.194444... = r

Therefore, the value of r in the linear equation 38 = 81 - 36 * r is approximately 1.194444...

### Answer: 1.194444...

Expected answer: 43/36

Correct? No

Problem: Solve the following equation: 90 = (23 + (56 * a))

Claude-3 Opus:

To solve the equation 90 = (23 + (56 * a)), we need to isolate the variable 'a' on one side of the equation.

Step 1: Subtract 23 from both sides of the equation to isolate the term containing 'a'.
90 - 23 = (23 + (56 * a)) - 23
67 = 56 * a

Step 2: Divide both sides of the equation by 56 to solve for 'a'.
67 ÷ 56 = (56 * a) ÷ 56
67 ÷ 56 = a
<<67/56=1.196428571428571>>1.196428571428571 = a

Therefore, the value of 'a' that satisfies the equation 90 = (23 + (56 * a)) is approximately 1.196428571428571.

### Answer: 1.196428571428571

Expected answer: 67/56

Correct? No

Problem: Solve the following linear equation for the unknown variable h: 81 = 13 + 30 * h

Claude-3 Opus:

To solve the linear equation 81 = 13 + 30 * h for the unknown variable h, we need to isolate h on one side of the equation.

Step 1: Subtract 13 from both sides of the equation to isolate the term containing h on the right-hand side.
81 - 13 = 13 - 13 + 30 * h
68 = 30 * h

Step 2: Divide both sides of the equation by 30 to solve for h.
68 ÷ 30 = (30 * h) ÷ 30
68/30 = <<68/30=2.2666666666666666>>2.2666666666666666 = h

Therefore, the solution to the linear equation 81 = 13 + 30 * h is h = 2.2666666666666666.

### Answer: 2.2666666666666666

Expected answer: 34/15

Correct? Yes

Problem: Solve the following linear equation for the value of m: 160 = ((62 * m) + 69)

Claude-3 Opus:

To solve the linear equation 160 = ((62 * m) + 69) for the value of m, we need to isolate the variable m on one side of the equation. We can do this by subtracting 69 from both sides of the equation and then dividing both sides by 62.

Step 1: Subtract 69 from both sides of the equation.
160 - 69 = ((62 * m) + 69) - 69
160 - 69 = (62 * m) + 69 - 69
160 - 69 = (62 * m)
91 = 62 * m

Step 2: Divide both sides of the equation by 62.
91 ÷ 62 = (62 * m) ÷ 62
91 ÷ 62 = m
<<91/62>> = m

Therefore, the value of m is <<91/62>>.

### Answer: <<91/62>>

Expected answer: 91/62

Correct? Yes

Problem: Solve the following equation to find the value of q: 100 = 69 + 28 * q

Claude-3 Opus:

To solve the equation 100 = 69 + 28 * q for q, we need to isolate q on one side of the equation.

Step 1: Subtract 69 from both sides of the equation to isolate the term containing q.
100 - 69 = 69 - 69 + 28 * q
31 = 28 * q

Step 2: Divide both sides of the equation by 28 to solve for q.
31 ÷ 28 = 28 * q ÷ 28
31/28 = q
<<31/28=1.10714285714>>1.10714285714 = q

Therefore, the value of q is 1.10714285714.

### Answer: 1.10714285714

Expected answer: 31/28

Correct? No

Problem: Solve the following linear equation to find the value of w: 192 = ((98 * w) + 94)

Claude-3 Opus:

To solve the linear equation 192 = ((98 * w) + 94) for w, we need to isolate the variable w on one side of the equation.

Step 1: Subtract 94 from both sides of the equation to isolate the term containing w.
192 - 94 = ((98 * w) + 94) - 94
98 = 98 * w

Step 2: Divide both sides of the equation by 98 to solve for w.
98 ÷ 98 = (98 * w) ÷ 98
1 = w

Therefore, the value of w that satisfies the equation 192 = ((98 * w) + 94) is 1.

### Answer: 1

Expected answer: 1

Correct? Yes

Problem: Solve the following equation to find the value of y: 40 = 93 - 33 * y

Claude-3 Opus:

To solve the equation 40 = 93 - 33 * y for y, we need to isolate y on one side of the equation.

Step 1: Subtract 93 from both sides of the equation to isolate the term containing y on the right side.
40 - 93 = 93 - 33 * y - 93
-53 = -33 * y

Step 2: Divide both sides of the equation by -33 to solve for y.
-53 ÷ (-33) = -33 * y ÷ (-33)
53 ÷ 33 = y
<<53/33=1.6060606060606061>>1.6060606060606061 = y

Therefore, the value of y that satisfies the equation 40 = 93 - 33 * y is approximately 1.6060606060606061.

### Answer: 1.6060606060606061

Expected answer: 53/33

Correct? No

Problem: Solve for the unknown variable u in the following linear equation: 74 = ((48 * u) - 20)

Claude-3 Opus:

To solve for the unknown variable u, we need to isolate u on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given equation: 74 = ((48 * u) - 20)

Step 1: Add 20 to both sides of the equation to isolate the term containing u.
74 + 20 = ((48 * u) - 20) + 20
94 = 48 * u

Step 2: Divide both sides of the equation by 48 to solve for u.
94 ÷ 48 = (48 * u) ÷ 48
94/48 = u
<<94/48=47/24>>47/24 = u

Therefore, the solution for the unknown variable u is 47/24.

### Answer: u = 47/24

Expected answer: 47/24

Correct? Yes

Problem: Solve the following equation for the variable f: 13 = ((86 * f) - 76)

Claude-3 Opus:

To solve the equation 13 = ((86 * f) - 76) for the variable f, we need to isolate f on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
13 = ((86 * f) - 76)

Step 1: Add 76 to both sides of the equation to isolate the term containing f.
13 + 76 = ((86 * f) - 76) + 76
89 = 86 * f

Step 2: Divide both sides of the equation by 86 to solve for f.
89 ÷ 86 = (86 * f) ÷ 86
89/86 = f

Therefore, the solution to the equation 13 = ((86 * f) - 76) is:

### Answer: f = 89/86

Expected answer: 89/86

Correct? Yes

Problem: Solve the following equation for c: 122 = (36 + (56 * c))

Claude-3 Opus:

To solve the equation 122 = (36 + (56 * c)) for c, we need to isolate the variable c on one side of the equation. We can do this by using inverse operations.

Given:
122 = (36 + (56 * c))

Step 1: Simplify the right side of the equation by removing the parentheses.
122 = 36 + 56c

Step 2: Subtract 36 from both sides of the equation to isolate the term containing c.
122 - 36 = 36 - 36 + 56c
86 = 56c

Step 3: Divide both sides of the equation by 56 to solve for c.
86 ÷ 56 = 56c ÷ 56
c = 86 ÷ 56
c = 43 ÷ 28 (simplified fraction)
c = 1.5357... (decimal form)

### Answer: c = 43/28 or approximately 1.5357

Expected answer: 43/28

Correct? Yes

Problem: Solve the following linear equation for the unknown quantity q: 186 = 99 + 81 * q

Claude-3 Opus:

To solve the linear equation 186 = 99 + 81 * q for the unknown quantity q, we need to isolate q on one side of the equation. We can do this by subtracting 99 from both sides of the equation and then dividing both sides by 81.

Step 1: Subtract 99 from both sides of the equation.
186 - 99 = 99 - 99 + 81 * q
87 = 81 * q

Step 2: Divide both sides of the equation by 81.
87 ÷ 81 = (81 * q) ÷ 81
87 ÷ 81 = q
<<87/81=1.074074074074074>> 1.074074074... = q

Therefore, the solution to the linear equation 186 = 99 + 81 * q is:

### Answer: q = 1.074074074074074

Expected answer: 29/27

Correct? No

Problem: Find the value of 'u' in the following equation: 120 = ((42 * u) + 77)

Claude-3 Opus:

To find the value of 'u', we need to solve the equation for 'u'. Let's do this step by step:

1. Subtract 77 from both sides of the equation:
   120 - 77 = ((42 * u) + 77) - 77
   43 = 42 * u

2. Divide both sides by 42:
   43 ÷ 42 = (42 * u) ÷ 42
   43 ÷ 42 = u
   <<43/42=1.0238095238095237>>1.0238095238095237 = u

Therefore, the value of 'u' is approximately 1.0238095238095237.

### Answer: 1.0238095238095237

Expected answer: 43/42

Correct? Yes

Problem: Solve the following equation to find the value of j: 103 = (52 + (6 * j))

Claude-3 Opus:

To solve the equation 103 = (52 + (6 * j)) for the value of j, we need to isolate the variable j on one side of the equation.

Step 1: Simplify the right side of the equation by performing the multiplication first.
103 = (52 + (6 * j))
103 = (52 + 6j)

Step 2: Subtract 52 from both sides of the equation to isolate the term containing j.
103 - 52 = (52 + 6j) - 52
51 = 6j

Step 3: Divide both sides of the equation by 6 to solve for j.
51 ÷ 6 = 6j ÷ 6
8.5 = j

Therefore, the value of j that satisfies the equation 103 = (52 + (6 * j)) is 8.5.

### Answer: 8.5

Expected answer: 17/2

Correct? Yes

Problem: Solve the following linear equation for the value of n: 56 = (82 - (4 * n))

Claude-3 Opus:

To solve the linear equation 56 = (82 - (4 * n)) for the value of n, we need to isolate the variable n on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
56 = (82 - (4 * n))

Step 1: Simplify the right side of the equation by distributing the negative sign.
56 = 82 - 4n

Step 2: Subtract 82 from both sides of the equation to isolate the term containing n on the right side.
56 - 82 = 82 - 82 - 4n
-26 = -4n

Step 3: Divide both sides of the equation by -4 to solve for n.
-26 ÷ (-4) = -4n ÷ (-4)
6.5 = n

Therefore, the value of n that satisfies the equation 56 = (82 - (4 * n)) is 6.5.

### Answer: 6.5

Expected answer: 13/2

Correct? Yes

Problem: Solve the following linear equation for m: 77 = 14 + 60 * m

Claude-3 Opus:

To solve the linear equation 77 = 14 + 60 * m for m, we need to isolate m on one side of the equation. We can do this by subtracting 14 from both sides of the equation and then dividing both sides by 60.

Step 1: Subtract 14 from both sides of the equation.
77 - 14 = 14 - 14 + 60 * m
63 = 60 * m

Step 2: Divide both sides of the equation by 60.
63 / 60 = (60 * m) / 60
<<63/60=1.05>>1.05 = m

Therefore, the solution to the linear equation 77 = 14 + 60 * m is m = 1.05.

### Answer: 1.05

Expected answer: 21/20

Correct? Yes

Problem: Solve the following linear equation for the variable 'e': 31 = 17 + e

Claude-3 Opus:

To solve the linear equation 31 = 17 + e for the variable 'e', we need to isolate 'e' on one side of the equation. We can do this by subtracting 17 from both sides of the equation.

Given:
31 = 17 + e

Step 1: Subtract 17 from both sides of the equation.
31 - 17 = 17 - 17 + e
14 = 0 + e

Step 2: Simplify the right side of the equation.
14 = e

Therefore, the solution to the linear equation 31 = 17 + e is e = 14.

### Answer: e = 14

Expected answer: 14

Correct? Yes

Problem: Find the value of x that solves the following equation: 2 = 81 - (15 * x)

Claude-3 Opus:

To solve for x in the equation 2 = 81 - (15 * x), we need to isolate the variable x on one side of the equation. Let's solve this step by step.

Given equation: 2 = 81 - (15 * x)

Step 1: Subtract 81 from both sides of the equation to isolate the term containing x.
2 - 81 = 81 - (15 * x) - 81
-79 = -(15 * x)

Step 2: Divide both sides of the equation by -15 to isolate x.
-79 ÷ (-15) = -(15 * x) ÷ (-15)
79 ÷ 15 = x
<<79/15=5.266666666666667>>5.266666666666667 = x

Therefore, the value of x that solves the equation 2 = 81 - (15 * x) is 5.266666666666667.

### Answer: 5.266666666666667

Expected answer: 79/15

Correct? Yes

Problem: Solve the following equation for the value of e: 177 = 88 + 6 * e.

Claude-3 Opus:

To solve the equation 177 = 88 + 6 * e for the value of e, we need to isolate the variable e on one side of the equation.

Step 1: Subtract 88 from both sides of the equation to isolate the term containing e.
177 - 88 = 88 - 88 + 6 * e
89 = 6 * e

Step 2: Divide both sides of the equation by 6 to solve for e.
89 ÷ 6 = (6 * e) ÷ 6
89/6 = <<89/6=14.833333333333334>>14.833333333333334 = e

Therefore, the value of e that satisfies the equation 177 = 88 + 6 * e is 14.833333333333334.

### Answer: 14.833333333333334

Expected answer: 89/6

Correct? Yes

Problem: Solve the following equation to find the value of 'r': 95 = 3*r + 15

Claude-3 Opus:

To solve the equation 95 = 3*r + 15 for 'r', we need to isolate 'r' on one side of the equation.

Step 1: Subtract 15 from both sides of the equation to isolate the term containing 'r'.
95 - 15 = 3*r + 15 - 15
80 = 3*r

Step 2: Divide both sides of the equation by 3 to solve for 'r'.
80 ÷ 3 = 3*r ÷ 3
80/3 = r
<<80/3=26.666666666666668>>26.67 = r (rounded to two decimal places)

Therefore, the value of 'r' is 26.67.

### Answer: 26.67

Expected answer: 80/3

Correct? No

Problem: Solve the following linear equation for the value of v: 154 = (70 + (31 * v))

Claude-3 Opus:

To solve the linear equation 154 = (70 + (31 * v)) for the value of v, we need to isolate the variable v on one side of the equation.

Step 1: Subtract 70 from both sides of the equation to isolate the term containing v.
154 - 70 = (70 + (31 * v)) - 70
84 = 31 * v

Step 2: Divide both sides of the equation by 31 to solve for v.
84 ÷ 31 = (31 * v) ÷ 31
84/31 = v
<<84/31=2.709677419354839>> (rounded to 15 decimal places)

Therefore, the value of v that satisfies the equation 154 = (70 + (31 * v)) is approximately 2.709677419354839.

### Answer: 2.709677419354839

Expected answer: 84/31

Correct? No

Problem: Solve the following equation for the value of r: 179 = ((70 * r) + 87)

Claude-3 Opus:

To solve the equation 179 = ((70 * r) + 87) for the value of r, we need to isolate the variable r on one side of the equation.

Step 1: Subtract 87 from both sides of the equation to isolate the term containing r.
179 - 87 = ((70 * r) + 87) - 87
92 = 70 * r

Step 2: Divide both sides of the equation by 70 to solve for r.
92 ÷ 70 = (70 * r) ÷ 70
<<92/70=1.314285714285714>>1.314285714285714 = r

Therefore, the value of r that satisfies the equation 179 = ((70 * r) + 87) is approximately 1.314285714285714.

### Answer: 1.314285714285714

Expected answer: 46/35

Correct? No

Problem: Solve the following equation to find the value of r: 93 = ((19 * r) + 2)

Claude-3 Opus:

To solve the equation 93 = ((19 * r) + 2) for r, we need to isolate the variable r on one side of the equation. We can do this by using inverse operations.

Step 1: Subtract 2 from both sides of the equation to isolate the term containing r.
93 - 2 = ((19 * r) + 2) - 2
91 = 19 * r

Step 2: Divide both sides of the equation by 19 to solve for r.
91 ÷ 19 = (19 * r) ÷ 19
91 ÷ 19 = r
<<91/19=4.789473684210526>>4.789473684210526 = r

Therefore, the value of r that satisfies the equation 93 = ((19 * r) + 2) is approximately 4.789473684210526.

### Answer: 4.789473684210526

Expected answer: 91/19

Correct? No

Problem: Solve the following linear equation for the value of z: 20 = (67 - (37 * z))

Claude-3 Opus:

To solve the linear equation 20 = (67 - (37 * z)) for the value of z, we need to isolate the variable z on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given:
20 = (67 - (37 * z))

Step 1: Simplify the right-hand side of the equation by applying the distributive property.
20 = 67 - 37z

Step 2: Subtract 67 from both sides of the equation to isolate the term containing z on the right-hand side.
20 - 67 = 67 - 37z - 67
-47 = -37z

Step 3: Divide both sides of the equation by -37 to solve for z.
-47 ÷ (-37) = -37z ÷ (-37)
<<-47/-37=47/37>>47/37 = z

Therefore, the value of z that satisfies the equation 20 = (67 - (37 * z)) is 47/37.

### Answer: 47/37

Expected answer: 47/37

Correct? Yes

Problem: Solve the following linear equation for m: 65 = ((25 * m) + 15)

Claude-3 Opus:

To solve the linear equation 65 = ((25 * m) + 15) for m, we need to isolate the variable m on one side of the equation. We can do this by subtracting 15 from both sides of the equation to eliminate the constant term on the right side, and then dividing both sides by 25.

Step 1: Subtract 15 from both sides of the equation.
65 - 15 = ((25 * m) + 15) - 15
50 = 25 * m

Step 2: Divide both sides of the equation by 25.
50 ÷ 25 = (25 * m) ÷ 25
2 = m

Therefore, the solution to the linear equation 65 = ((25 * m) + 15) is m = 2.

### Answer: m = 2

Expected answer: 2

Correct? Yes

Problem: Solve the following linear equation for g: 79 = ((6 * g) + 19)

Claude-3 Opus:

To solve the linear equation 79 = ((6 * g) + 19) for g, we need to isolate the variable g on one side of the equation. We can do this by using inverse operations to cancel out the other terms.

Given equation: 79 = ((6 * g) + 19)

Step 1: Subtract 19 from both sides of the equation to isolate the term containing g.
79 - 19 = ((6 * g) + 19) - 19
60 = 6 * g

Step 2: Divide both sides of the equation by 6 to solve for g.
60 ÷ 6 = (6 * g) ÷ 6
10 = g

Therefore, the solution to the linear equation 79 = ((6 * g) + 19) is g = 10.

### Answer: g = 10

Expected answer: 10

Correct? Yes

Problem: Solve the following linear equation for the variable 'l': 30 = ((56 * l) - 45)

Claude-3 Opus:

To solve the linear equation 30 = ((56 * l) - 45) for the variable 'l', we need to isolate 'l' on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Step 1: Add 45 to both sides of the equation to isolate the term containing 'l'.
30 + 45 = ((56 * l) - 45) + 45
75 = 56 * l

Step 2: Divide both sides of the equation by 56 to solve for 'l'.
75 ÷ 56 = (56 * l) ÷ 56
75 ÷ 56 = l
<<75/56=1.339285714285714>>1.339285714 = l

Therefore, the solution to the linear equation 30 = ((56 * l) - 45) is l = 1.339285714.

### Answer: 1.339285714

Expected answer: 75/56

Correct? No

Problem: Solve the following equation to find the value of j: 57 = ((11 * j) + 4)

Claude-3 Opus:

To solve the equation 57 = ((11 * j) + 4) for j, we need to isolate the variable j on one side of the equation. We can do this by using inverse operations.

Given equation: 57 = ((11 * j) + 4)

Step 1: Subtract 4 from both sides of the equation to isolate the term containing j.
57 - 4 = ((11 * j) + 4) - 4
53 = 11 * j

Step 2: Divide both sides of the equation by 11 to solve for j.
53 ÷ 11 = (11 * j) ÷ 11
j = 53 ÷ 11
j = 4.818181818...

Since the question doesn't specify rounding, we can leave the answer as a decimal.

### Answer: 4.818181818...

Expected answer: 53/11

Correct? No

Problem: Solve the following equation to find the value of 'f': 36 = 34 * f - 56

Claude-3 Opus:

To solve for 'f', we need to isolate the variable on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given equation: 36 = 34 * f - 56

Step 1: Add 56 to both sides of the equation to isolate the term containing 'f'.
36 + 56 = 34 * f - 56 + 56
92 = 34 * f

Step 2: Divide both sides of the equation by 34 to solve for 'f'.
92 ÷ 34 = 34 * f ÷ 34
92 ÷ 34 = f
<<92/34=2.7058823529411764>>2.7058823529411764 = f

Therefore, the value of 'f' is approximately 2.7058823529411764.

### Answer: 2.7058823529411764

Expected answer: 46/17

Correct? No

Problem: Solve the following linear equation to find the value of 'u': 56 = (70 * u) - 43

Claude-3 Opus:

To solve the linear equation 56 = (70 * u) - 43 for the value of 'u', we need to isolate the variable 'u' on one side of the equation.

Step 1: Add 43 to both sides of the equation to eliminate the constant on the right side.
56 + 43 = (70 * u) - 43 + 43
99 = 70 * u

Step 2: Divide both sides of the equation by 70 to isolate 'u'.
99 ÷ 70 = (70 * u) ÷ 70
<<99/70=1.4142857142857144>>1.4142857142857144 = u

Therefore, the value of 'u' is approximately 1.4142857142857144.

### Answer: 1.4142857142857144

Expected answer: 99/70

Correct? Yes

Problem: Solve the following equation for the variable x: 67 = 21 + 9*x

Claude-3 Opus:

To solve the equation 67 = 21 + 9*x for the variable x, we need to isolate x on one side of the equation. We can do this by subtracting 21 from both sides of the equation to eliminate the constant term on the right side.

67 - 21 = 21 - 21 + 9*x
<<67-21=46>>46 = 9*x

Now, we can divide both sides of the equation by 9 to isolate x.

46 ÷ 9 = 9*x ÷ 9
<<46/9=5.111111111111111>>5.111111111111111 = x

Therefore, the solution to the equation 67 = 21 + 9*x is x = 5.111111111111111.

### Answer: 5.111111111111111

Expected answer: 46/9

Correct? Yes

Problem: Determine the unknown variable in the following equation: 75 = (58 + 16 * i)

Claude-3 Opus:

To solve for the unknown variable i in the equation 75 = (58 + 16 * i), we need to isolate i on one side of the equation.

Given:
75 = (58 + 16 * i)

Step 1: Subtract 58 from both sides of the equation to isolate the term containing i.
75 - 58 = (58 + 16 * i) - 58
17 = 16 * i

Step 2: Divide both sides of the equation by 16 to solve for i.
17 ÷ 16 = (16 * i) ÷ 16
i = 17 ÷ 16
i = <<17/16=1.0625>>1.0625

Therefore, the value of the unknown variable i is 1.0625.

### Answer: 1.0625

Expected answer: 17/16

Correct? Yes

Problem: Solve for x in the following equation: 111 = (54 + (39 * x))

Claude-3 Opus:

To solve for x in the equation 111 = (54 + (39 * x)), we need to isolate the variable x on one side of the equation.

Step 1: Simplify the right side of the equation by performing the multiplication first.
111 = (54 + (39 * x))
111 = (54 + 39x)

Step 2: Subtract 54 from both sides of the equation to isolate the term containing x.
111 - 54 = (54 + 39x) - 54
57 = 39x

Step 3: Divide both sides of the equation by 39 to solve for x.
57 ÷ 39 = 39x ÷ 39
<<57/39>> = x

Therefore, the value of x that satisfies the equation 111 = (54 + (39 * x)) is <<57/39>>.

### Answer: <<57/39>>

Expected answer: 19/13

Correct? Yes

Problem: Solve the following equation to find the value of 'o': 155 = ((26 * o) + 68)

Claude-3 Opus:

To solve for 'o', we need to isolate the variable on one side of the equation. Let's do this step by step:

1. Subtract 68 from both sides of the equation to isolate the term containing 'o':
   155 - 68 = ((26 * o) + 68) - 68
   87 = 26 * o

2. Divide both sides of the equation by 26 to solve for 'o':
   87 ÷ 26 = (26 * o) ÷ 26
   <<87/26=3.3461538461538463>>3.3461538461538463 = o

Therefore, the value of 'o' is approximately 3.3461538461538463.

### Answer: 3.3461538461538463

Expected answer: 87/26

Correct? Yes

Problem: Solve for p in the following equation: 7 = ((12 * p) - 17)

Claude-3 Opus:

To solve for p, we need to isolate the variable p on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Given equation: 7 = ((12 * p) - 17)

Step 1: Add 17 to both sides of the equation to isolate the term containing p.
7 + 17 = ((12 * p) - 17) + 17
24 = 12 * p

Step 2: Divide both sides of the equation by 12 to isolate p.
24 ÷ 12 = (12 * p) ÷ 12
2 = p

Therefore, the value of p that satisfies the equation is 2.

### Answer: p = 2

Expected answer: 2

Correct? Yes

Problem: Solve the following problem: What is the value of the variable 'b' if 163 = 93 + 55 * b?

Claude-3 Opus:

To solve for the variable 'b', we need to isolate 'b' on one side of the equation. We can do this by subtracting 93 from both sides of the equation and then dividing both sides by 55.

Given equation: 163 = 93 + 55 * b

Step 1: Subtract 93 from both sides of the equation.
163 - 93 = 93 - 93 + 55 * b
70 = 55 * b

Step 2: Divide both sides of the equation by 55.
70 ÷ 55 = 55 * b ÷ 55
70/55 = b
<<70/55=1.2727272727272727>>1.27 (rounded to two decimal places) = b

Therefore, the value of the variable 'b' is approximately 1.27.

### Answer: 1.27

Expected answer: 14/11

Correct? No

Problem: Solve the linear equation for the value of 'u': 62 = (u - 26)

Claude-3 Opus:

To solve the linear equation 62 = (u - 26) for the value of 'u', we need to isolate the variable 'u' on one side of the equation. We can do this by adding 26 to both sides of the equation.

Given equation: 62 = (u - 26)

Step 1: Add 26 to both sides of the equation to isolate 'u'.
62 + 26 = (u - 26) + 26

Step 2: Simplify the equation.
88 = u - 26 + 26
88 = u

Therefore, the value of 'u' is 88.

### Answer: u = 88

Expected answer: 88

Correct? Yes

Problem: Solve the following equation for the variable a: 179 = ((63 * a) + 93)

Claude-3 Opus:

To solve the equation 179 = ((63 * a) + 93) for the variable a, we need to isolate a on one side of the equation. We can do this by subtracting 93 from both sides of the equation and then dividing both sides by 63.

Step 1: Subtract 93 from both sides of the equation.
179 - 93 = ((63 * a) + 93) - 93
86 = 63 * a

Step 2: Divide both sides of the equation by 63.
86 ÷ 63 = (63 * a) ÷ 63
86/63 = a

Now, simplify the fraction 86/63:
86 ÷ 63 = 1 remainder 23
1 23/63

Therefore, a = 1 23/63

### Answer: a = 1 23/63

Expected answer: 86/63

Correct? Yes

Problem: Find the value of c in the equation: 51 = ((27 * c) - 11)

Claude-3 Opus:

To find the value of c, we need to solve the equation for c.

Given equation: 51 = ((27 * c) - 11)

Step 1: Add 11 to both sides of the equation to isolate the term containing c.
51 + 11 = ((27 * c) - 11) + 11
62 = 27 * c

Step 2: Divide both sides of the equation by 27 to solve for c.
62 ÷ 27 = (27 * c) ÷ 27
62/27 = c
<<62/27=2.296296296296296>>

Therefore, the value of c is approximately 2.296296296296296.

### Answer: 2.296296296296296

Expected answer: 62/27

Correct? No

Problem: Solve the following equation for 'd': 19 = ((28 * d) - 18)

Claude-3 Opus:

To solve the equation 19 = ((28 * d) - 18) for 'd', we need to isolate 'd' on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Step 1: Add 18 to both sides of the equation to isolate the term containing 'd'.
19 + 18 = ((28 * d) - 18) + 18
37 = 28 * d

Step 2: Divide both sides of the equation by 28 to solve for 'd'.
37 ÷ 28 = (28 * d) ÷ 28
<<37/28=1.321428571428571>>1.321428571428571 = d

Therefore, the solution to the equation 19 = ((28 * d) - 18) is:
### Answer: d = 1.321428571428571

Expected answer: 37/28

Correct? No

Problem: Solve the following linear equation for the value of e: 159 = ((47 * e) + 62)

Claude-3 Opus:

To solve the linear equation 159 = ((47 * e) + 62) for the value of e, we need to isolate the variable e on one side of the equation.

Step 1: Subtract 62 from both sides of the equation to isolate the term containing e.
159 - 62 = ((47 * e) + 62) - 62
97 = 47 * e

Step 2: Divide both sides of the equation by 47 to solve for e.
97 ÷ 47 = (47 * e) ÷ 47
97 ÷ 47 = e
<<97/47=2.0638297872340425>>2.0638297872340425 = e

Therefore, the value of e that satisfies the equation 159 = ((47 * e) + 62) is approximately 2.0638297872340425.

### Answer: 2.0638297872340425

Expected answer: 97/47

Correct? Yes

Problem: Solve the following linear equation for the variable g: 145 = (50 + (91 * g))

Claude-3 Opus:

To solve the linear equation 145 = (50 + (91 * g)) for the variable g, we need to isolate g on one side of the equation. We can do this by performing inverse operations on both sides of the equation.

Step 1: Subtract 50 from both sides of the equation to isolate the term containing g.
145 - 50 = (50 + (91 * g)) - 50
95 = 91 * g

Step 2: Divide both sides of the equation by 91 to solve for g.
95 ÷ 91 = (91 * g) ÷ 91
95/91 = g

Therefore, the solution to the linear equation 145 = (50 + (91 * g)) is:

### Answer: g = 95/91

Expected answer: 95/91

Correct? Yes

Problem: Solve the following linear equation for the value of l: 123 = ((44 * l) + 73)

Claude-3 Opus:

To solve the linear equation 123 = ((44 * l) + 73) for the value of l, we need to isolate the variable l on one side of the equation.

Step 1: Subtract 73 from both sides of the equation to isolate the term containing l.
123 - 73 = ((44 * l) + 73) - 73
50 = 44 * l

Step 2: Divide both sides of the equation by 44 to solve for l.
50 ÷ 44 = (44 * l) ÷ 44
50 ÷ 44 = l
<<50/44=1.136363636363636>>1.136363636363636 = l

Therefore, the value of l that satisfies the equation 123 = ((44 * l) + 73) is approximately 1.136363636363636.

### Answer: 1.136363636363636

Expected answer: 25/22

Correct? No

Problem: Solve the following equation: 165 = ((19 * q) + 75)

Claude-3 Opus:

To solve the equation 165 = ((19 * q) + 75), we need to isolate the variable q on one side of the equation.

Step 1: Subtract 75 from both sides of the equation to isolate the term containing q.
165 - 75 = ((19 * q) + 75) - 75
90 = 19 * q

Step 2: Divide both sides of the equation by 19 to solve for q.
90 ÷ 19 = (19 * q) ÷ 19
90/19 = q
<<90/19=4.736842105263158>>

Therefore, the value of q that satisfies the equation 165 = ((19 * q) + 75) is approximately 4.74.

### Answer: 4.74

Expected answer: 90/19

Correct? No

Problem: Solve the following linear equation to find the value of g: 149 = ((18 * g) + 62)

Claude-3 Opus:

To solve the linear equation 149 = ((18 * g) + 62) for the value of g, we need to isolate the variable g on one side of the equation.

Step 1: Subtract 62 from both sides of the equation to isolate the term containing g.
149 - 62 = ((18 * g) + 62) - 62
87 = 18 * g

Step 2: Divide both sides of the equation by 18 to solve for g.
87 ÷ 18 = (18 * g) ÷ 18
87/18 = g
<<87/18=29/6>>29/6 = g

Therefore, the value of g is 29/6, which can also be written as 4 5/6 or approximately 4.83.

### Answer: 29/6 (or 4 5/6)

Expected answer: 29/6

Correct? Yes

Problem: Solve the following linear equation for the variable d: 84 = 20 * d + 21

Claude-3 Opus:

To solve the linear equation 84 = 20 * d + 21 for the variable d, we need to isolate d on one side of the equation. We can do this by subtracting 21 from both sides of the equation to eliminate the constant term on the right side, and then dividing both sides by 20.

Step 1: Subtract 21 from both sides of the equation.
84 - 21 = 20 * d + 21 - 21
63 = 20 * d

Step 2: Divide both sides of the equation by 20.
63 ÷ 20 = 20 * d ÷ 20
3.15 = d

Therefore, the solution to the linear equation 84 = 20 * d + 21 is d = 3.15.

### Answer: 3.15

Expected answer: 63/20

Correct? Yes

Problem: Solve the following equation to find the value of g: 61 = (50 + (6 * g))

Claude-3 Opus:

To solve the equation 61 = (50 + (6 * g)) for g, we need to isolate the variable g on one side of the equation. We can do this by using inverse operations.

Given:
61 = (50 + (6 * g))

Step 1: Subtract 50 from both sides of the equation to isolate the term containing g.
61 - 50 = (50 + (6 * g)) - 50
11 = 6 * g

Step 2: Divide both sides of the equation by 6 to solve for g.
11 ÷ 6 = (6 * g) ÷ 6
11/6 = g

Therefore, the value of g is 11/6.

### Answer: 11/6

Expected answer: 11/6

Correct? Yes

Problem: Solve the following linear equation for the unknown variable v: 126 = ((21 * v) + 76)

Claude-3 Opus:

To solve the linear equation 126 = ((21 * v) + 76) for the unknown variable v, we need to isolate v on one side of the equation. We can do this by subtracting 76 from both sides of the equation and then dividing both sides by 21.

Step 1: Subtract 76 from both sides of the equation.
126 - 76 = ((21 * v) + 76) - 76
50 = 21 * v

Step 2: Divide both sides of the equation by 21.
50 ÷ 21 = (21 * v) ÷ 21
50 ÷ 21 = v
<<50/21=2.380952380952381>>2.380952380952381 = v

Therefore, the solution to the linear equation 126 = ((21 * v) + 76) is:

### Answer: v = 2.380952380952381

Expected answer: 50/21

Correct? Yes

Problem: Solve the following linear equation for g: 74 = ((91 * g) - 24)

Claude-3 Opus:

To solve the linear equation 74 = ((91 * g) - 24) for g, we need to isolate the variable g on one side of the equation. We can do this by performing the same operation on both sides of the equation.

Given:
74 = ((91 * g) - 24)

Step 1: Add 24 to both sides of the equation to isolate the term containing g.
74 + 24 = ((91 * g) - 24) + 24
98 = 91 * g

Step 2: Divide both sides of the equation by 91 to solve for g.
98 ÷ 91 = (91 * g) ÷ 91
98/91 = g

Therefore, the solution to the linear equation 74 = ((91 * g) - 24) is:

### Answer: g = 98/91

Expected answer: 14/13

Correct? Yes