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

Claude-3 Sonnet:

To solve the equation 122 = 92 + 28 * u for the variable u, we need to isolate u on one side of the equation.

Given equation: 122 = 92 + 28 * u

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

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

Step 3: Simplify the fraction on the right-hand side.
u = 15 / 14

Therefore, the solution to the equation 122 = 92 + 28 * u is u = 15 / 14.

### Answer: 15/14

Expected answer: 15/14

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation 42 = ((35 * i) - 34) for i, we need to perform the following steps:

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

Step 2: Divide both sides of the equation by 35 to get the value of i.
76 / 35 = 35 * i / 35
i = 76 / 35
i = 2.171428571...

Therefore, the value of i that satisfies the equation 42 = ((35 * i) - 34) is approximately 2.171428571.

### Answer: 2.171428571

Expected answer: 76/35

Correct? No

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

Claude-3 Sonnet:

To solve the equation 94 = 41 + 6 * r for r, we need to isolate r on one side of the equation.

Given equation: 94 = 41 + 6 * r

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

Step 2: Divide both sides of the equation by 6 to find the value of r.
53 / 6 = 6 * r / 6
r = 8.83

Therefore, the value of r in the equation 94 = 41 + 6 * r is 8.83.

### Answer: 8.83

Expected answer: 53/6

Correct? No

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

Claude-3 Sonnet:

To solve this equation for i, we need to isolate i on one side of the equation.

Given equation: 158 = ((19 * i) + 94)

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

Step 2: Divide both sides of the equation by 19 to find the value of i.
64 / 19 = 19 * i / 19
i = 64 / 19
i = 3.368421...

Therefore, the value of i is approximately 3.37.

### Answer: 3.37

Expected answer: 64/19

Correct? No

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

Claude-3 Sonnet:

To solve the equation for 'q', we need to isolate 'q' on one side of the equation.

Given equation: 134 = ((30 * q) + 54)

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

Step 2: Divide both sides of the equation by 30 to get the value of 'q'.
80 / 30 = 30 * q / 30
q = 80 / 30
q = 8/3

Therefore, the value of 'q' that satisfies the equation 134 = ((30 * q) + 54) is 8/3.

### Answer: 8/3

Expected answer: 8/3

Correct? Yes

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

Claude-3 Sonnet:

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

Given equation: 94 = (27 + y)

Step 1: Remove the parentheses by distributing the value outside the parentheses.
94 = 27 + y

Step 2: Subtract 27 from both sides of the equation to isolate y.
94 - 27 = 27 + y - 27
67 = y

Therefore, the value of y that satisfies the equation 94 = (27 + y) is 67.

### Answer: 67

Expected answer: 67

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation 9 = ((23 * h) - 70) for the value of h, we need to perform the following steps:

Step 1: Isolate the term containing h on one side of the equation.
9 = (23 * h) - 70
9 + 70 = (23 * h) - 70 + 70
79 = 23 * h

Step 2: Divide both sides of the equation by 23 to get the value of h.
79 / 23 = (23 * h) / 23
79 / 23 = h

Step 3: Perform the division to find the value of h.
79 / 23 ≈ 3.43478...

Therefore, the value of h in the equation 9 = ((23 * h) - 70) is approximately 3.43478.

### Answer: 3.43478

Expected answer: 79/23

Correct? No

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

Claude-3 Sonnet:

To solve the equation 92 = 33 * t + 26 for the value of t, we need to isolate t on one side of the equation.

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

Step 2: Divide both sides of the equation by 33 to isolate t.
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 Sonnet:

To solve the linear equation 123 = ((15 * e) + 29) for the value of e, we need to perform the following steps:

Step 1: Isolate the term containing the variable e on one side of the equation.
123 = (15 * e) + 29
123 - 29 = (15 * e) + 29 - 29
94 = 15 * e

Step 2: Divide both sides of the equation by 15 to get the value of e.
94 / 15 = 15 * e / 15
e = 94 / 15
e = 6.26666...

Therefore, the value of e in the given linear equation is approximately 6.27.

### Answer: 6.27

Expected answer: 94/15

Correct? No

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

Claude-3 Sonnet:

To solve for the value of k, we need to isolate k on one side of the equation.

Given equation: 16 = (75 * k) - 80

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

Step 2: Divide both sides of the equation by 75 to find the value of k.
96/75 = 75 * k / 75
k = 96/75
k = 1.28

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 Sonnet:

To solve for q in the equation 131 = ((5 * q) + 89), we need to isolate q on one side of the equation.

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

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

Step 2: Divide both sides of the equation by 5 to get q alone.
42 / 5 = 5 * q / 5
q = 8.4

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 Sonnet:

To find the value of p that satisfies the equation 147 = ((38 * p) + 56), we need to isolate p on one side of the equation.

Given equation: 147 = ((38 * p) + 56)

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

Step 2: Divide both sides of the equation by 38 to find the value of p.
91 / 38 = 38 * p / 38
p = 2.39473684210526

Therefore, the value of p that satisfies the equation 147 = ((38 * p) + 56) is approximately 2.39.

### Answer: 2.39

Expected answer: 91/38

Correct? No

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

Claude-3 Sonnet:

To solve the equation 76 = 42 * j + 23 for the value of j, we need to isolate j on one side of the equation.

Step 1: Subtract 23 from both sides of the equation to get rid of the constant term.
76 - 23 = 42 * j + 23 - 23
53 = 42 * j

Step 2: Divide both sides of the equation by 42 to isolate j.
53 / 42 = 42 * j / 42
j = 53 / 42

Step 3: Evaluate the expression on the right-hand side.
53 / 42 = 1.2619047619047619

Therefore, the value of j is approximately 1.2619047619047619.

### Answer: 1.2619047619047619

Expected answer: 53/42

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation for the value of 'l', we need to isolate 'l' on one side of the equation.

Given equation: 138 = 43 + 25 * l

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

Step 2: Divide both sides of the equation by 25.
95 / 25 = 25 * l / 25
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 Sonnet:

To solve the equation 80 = ((24 * w) + 35) for the unknown w, we need to isolate w on one side of the equation.

Given equation: 80 = ((24 * w) + 35)

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

Step 2: Divide both sides of the equation by 24 to find the value of w.
45 / 24 = 24 * w / 24
w = 45 / 24
w = 1.875

Therefore, the value of the unknown 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 Sonnet:

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

Given equation: 77 = (33 + (14 * x))

Step 1: Remove the parentheses by distributing the multiplication.
77 = 33 + 14x

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

Step 3: Divide both sides of the equation by 14 to find the value of x.
44/14 = 14x/14
x = 44/14
x = 3.14285714286

Therefore, the value of x that satisfies the equation 77 = (33 + (14 * x)) is approximately 3.14.

### Answer: 3.14

Expected answer: 22/7

Correct? No

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

Claude-3 Sonnet:

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 get rid of the constant term on the right-hand side.
110 - 12 = 12 + 88 * y - 12
98 = 88 * y

Step 2: Divide both sides of the equation by 88 to isolate y.
98 / 88 = 88 * y / 88
y = 1.114

Therefore, the value of y that satisfies the equation 110 = 12 + 88 * y is approximately 1.114.

### Answer: 1.114

Expected answer: 49/44

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 179 = 82 * s + 80 for the variable s, we need to isolate s on one side of the equation.

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

Step 2: Divide both sides of the equation by 82 to isolate s.
99 / 82 = 82 * s / 82
s = 99 / 82

Step 3: Evaluate the division to find the value of s.
s = 1.2073170731707318

Therefore, the solution to the linear equation 179 = 82 * s + 80 is s = 1.2073170731707318.

### Answer: 1.2073170731707318

Expected answer: 99/82

Correct? No

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

Claude-3 Sonnet:

To solve the equation 129 = 26 * m + 66 for m, we need to isolate m on one side of the equation.

Step 1: Subtract 66 from both sides of the equation to get rid of the constant term on the right-hand side.
129 - 66 = 26 * m + 66 - 66
63 = 26 * m

Step 2: Divide both sides of the equation by 26 to isolate m.
63 / 26 = 26 * m / 26
m = 63 / 26

Step 3: Simplify the fraction on the right-hand side.
63 / 26 = 2 (with a remainder of 11)
m = 2 + 11/26

Therefore, the solution to the equation 129 = 26 * m + 66 is m = 2 + 11/26.

### Answer: 2 + 11/26

Expected answer: 63/26

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation 82 = ((27 * q) - 17) for q, we need to perform the following steps:

Step 1: Isolate the term containing q on one side of the equation.
82 = (27 * q) - 17
82 + 17 = (27 * q) - 17 + 17
99 = 27 * q

Step 2: Divide both sides of the equation by 27 to get q alone.
99 / 27 = (27 * q) / 27
99 / 27 = q

Step 3: Perform the division to find the value of q.
99 / 27 = 3.67

Therefore, the solution to the linear equation 82 = ((27 * q) - 17) is q = 3.67.

### Answer: 3.67

Expected answer: 11/3

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation for the variable k, we need to isolate k on one side of the equation by performing inverse operations.

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

Step 1: Remove the parentheses by distributing the multiplication.
141 = 64 + 22k

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

Step 3: Divide both sides of the equation by 22 to find the value of k.
77/22 = 22k/22
k = 3.5

Therefore, the value of k that satisfies the given linear equation is 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 Sonnet:

To solve this linear equation for the value of v, we need to isolate v on one side of the equation.

Given equation: 175 = 91 + 45 * v

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

Step 2: Divide both sides of the equation by 45.
84 / 45 = 45 * v / 45
v = 84 / 45
v = 1.8666...

Therefore, the value of v that satisfies the linear equation 175 = 91 + 45 * v is approximately 1.87.

### Answer: 1.87

Expected answer: 28/15

Correct? No

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

Claude-3 Sonnet:

To solve for the value of k, we need to isolate k on one side of the equation.

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

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

Step 2: Divide both sides of the equation by 63 to isolate k.
68 / 63 = (63 * k) / 63
k = 68 / 63

Step 3: Evaluate the division to find the value of k.
k = 1.0793650793650793

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 Sonnet:

To solve the equation 65 = ((8 * l) - 10) for l, we need to perform the following steps:

Step 1: Isolate the term with the variable l by performing inverse operations on both sides of the equation.
65 = (8 * l) - 10
65 + 10 = (8 * l) - 10 + 10 (Adding 10 to both sides)
75 = 8 * l

Step 2: Divide both sides of the equation by 8 to isolate l.
75 / 8 = (8 * l) / 8
l = 75 / 8

Step 3: Evaluate the expression on the right-hand side.
l = 75 / 8
l = 9.375

Therefore, the value of l that satisfies the equation 65 = ((8 * l) - 10) is 9.375.

### Answer: 9.375

Expected answer: 75/8

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation 5 = ((10 * u) - 34), we need to isolate the variable u.

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

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

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 Sonnet:

To solve the linear equation 91 = 9a + 61 for the variable 'a', we need to isolate 'a' on one side of the equation.

Given equation: 91 = 9a + 61

Step 1: Subtract 61 from both sides of the equation to isolate the term with 'a'.
91 - 61 = 9a + 61 - 61
30 = 9a

Step 2: Divide both sides of the equation by 9 to get the value of 'a'.
30/9 = 9a/9
a = 30/9
a = 10/3

Therefore, the solution to the linear equation 91 = 9a + 61 is a = 10/3.

### Answer: 10/3

Expected answer: 10/3

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation 157 = 53 * i + 61 for the variable i, we need to isolate i on one side of the equation by performing inverse operations.

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

Step 2: Divide both sides of the equation by 53 to isolate i.
96 / 53 = 53 * i / 53
i = 96 / 53
i = 1.8113207547169812 (approximately)

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

### Answer: 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 Sonnet:

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.

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

Step 2: Divide both sides of the equation by 24 to isolate q.
57 / 24 = 24 * q / 24
q = 57 / 24

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.
q = (57 / 3) / (24 / 3)
q = 19 / 8

Therefore, the value of q that satisfies the linear equation 71 = ((24 * q) + 14) is q = 19 / 8.

### Answer: 19/8

Expected answer: 19/8

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation for the value of i, we need to isolate i on one side of the equation.

Given equation: 163 = 96 + 14 * i

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

Step 2: Divide both sides of the equation by 14.
67 / 14 = 14 * i / 14
i = 4.79

Therefore, the value of i that satisfies the linear equation 163 = 96 + 14 * i is approximately 4.79.

### Answer: 4.79

Expected answer: 67/14

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 59 = (70 * e) - 23 for the value of e, we need to perform the following steps:

Step 1: Isolate the term containing the variable e by moving all the constant terms to the other side of the equation.
59 + 23 = (70 * e)
82 = (70 * e)

Step 2: Divide both sides of the equation by the coefficient of e, which is 70.
82 / 70 = (70 * e) / 70
(82 / 70) = e

Step 3: Perform the division to find the value of e.
(82 / 70) = 1.1714285714285715

Therefore, the value of e that satisfies the equation 59 = (70 * e) - 23 is approximately 1.1714285714285715.

### Answer: 1.1714285714285715

Expected answer: 41/35

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation 147 = 36 * o + 74 for o, we need to isolate the variable o on one side of the equation.

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

Step 2: Divide both sides of the equation by 36 to isolate the variable o.
73 / 36 = 36 * o / 36
2 = o

Therefore, the solution to the linear equation 147 = 36 * o + 74 is o = 2.

### Answer: 2

Expected answer: 73/36

Correct? No

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

Claude-3 Sonnet:

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

Step 1: Subtract 93 from both sides of the equation.
71 - 93 = 93 - (13 * d) - 93
-22 = -13d

Step 2: Divide both sides of the equation by -13.
-22/-13 = -13d/-13
d = 22/13

Therefore, the solution to the equation 71 = 93 - (13 * d) is d = 22/13.

### Answer: 22/13

Expected answer: 22/13

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation 118 = 64 + 6 * n for n, we need to isolate n on one side of the equation.

Given equation: 118 = 64 + 6 * n

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

To solve the equation 61 = ((5 * d) - 7) for the value of d, we need to perform the following steps:

Step 1: Simplify the right-hand side of the equation by removing the parentheses.
61 = (5 * d) - 7

Step 2: Add 7 to both sides of the equation to isolate the term with d.
61 + 7 = (5 * d) - 7 + 7
68 = 5 * d

Step 3: Divide both sides of the equation by 5 to find the value of d.
68 / 5 = 5 * d / 5
d = 13.6

Therefore, the value of d in the equation 61 = ((5 * d) - 7) 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 Sonnet:

To solve the linear equation 79 = ((8 * z) - 18) for the value of z, we need to perform the following steps:

Step 1: Simplify the right-hand side of the equation by removing the parentheses.
79 = (8 * z) - 18

Step 2: Add 18 to both sides of the equation to isolate the term with z.
79 + 18 = (8 * z) - 18 + 18
97 = 8 * z

Step 3: Divide both sides of the equation by 8 to find the value of z.
97 / 8 = 8 * z / 8
z = 12.125

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 Sonnet:

To solve the linear equation 129 = ((2 * z) + 63) for the value of z, we need to perform the following steps:

Step 1: Remove the parentheses by distributing the multiplication.
129 = (2 * z) + 63

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

Step 3: Divide both sides of the equation by 2 to get the value of z.
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 Sonnet:

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

Given equation: 127 = (29 + (32 * e))

Step 1: Remove the parentheses by distributing 32.
127 = 29 + 32e

Step 2: Subtract 29 from both sides of the equation.
127 - 29 = 32e
98 = 32e

Step 3: Divide both sides of the equation by 32.
98/32 = 32e/32
e = 98/32
e = 3.0625

Therefore, the value of e that satisfies the equation 127 = (29 + (32 * e)) is 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 Sonnet:

To solve the linear equation 30 = ((50 * x) - 35) for the value of x, we need to perform the following steps:

Step 1: Remove the parentheses by combining like terms on the right-hand side.
30 = 50x - 35

Step 2: Add 35 to both sides of the equation to isolate the term with x.
30 + 35 = 50x - 35 + 35
65 = 50x

Step 3: Divide both sides of the equation by 50 to find the value of x.
65/50 = 50x/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 Sonnet:

To solve the equation 66 = 9 + 10 * x for x, we need to isolate x on one side of the equation.

Given equation: 66 = 9 + 10 * x

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

Step 2: Divide both sides of the equation by 10 to get x alone.
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 Sonnet:

To solve the equation for the unknown variable a, we need to isolate a on one side of the equation.

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

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

Step 2: Divide both sides of the equation by 38 to get the value of a.
52 / 38 = (38 * a) / 38
a = 52 / 38

Step 3: Evaluate the division to find the value of a.
a = 1.368421...

Therefore, the value of the unknown variable a in the equation 103 = ((38 * a) + 51) is approximately 1.368421.

### Answer: 1.368421

Expected answer: 26/19

Correct? No

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

Claude-3 Sonnet:

To solve this equation for f, we need to isolate f on one side of the equation.

Given equation: 105 = 28 * f + 8

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

Step 2: Divide both sides of the equation by 28 to find the value of f.
97 / 28 = 28 * f / 28
f = 97 / 28
f = 3.464285714285714

Therefore, the value of f in the equation 105 = 28 * f + 8 is approximately 3.464285714285714.

### Answer: 3.464285714285714

Expected answer: 97/28

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation for u, we need to isolate u on one side of the equation by performing inverse operations.

Given equation: 12 = 63 - 50u

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

Step 2: Divide both sides of the equation by -50 to isolate u.
-51/-50 = -50u/-50
u = 1.02

Therefore, the solution to the linear equation 12 = 63 - 50u is u = 1.02.

### Answer: 1.02

Expected answer: 51/50

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation for the value of 'b', we need to isolate 'b' on one side of the equation.

Given equation: 60 = 42 + (10 * b)

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

Step 2: Divide both sides of the equation by 10.
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 Sonnet:

To solve the linear equation 84 = ((25 * j) + 13) for the variable 'j', we need to isolate 'j' on one side of the equation by performing inverse operations.

Given equation: 84 = ((25 * j) + 13)

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

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

Step 3: Evaluate the left-hand side.
71 / 25 = 2.84

Therefore, the value of 'j' that satisfies the equation 84 = ((25 * j) + 13) is 2.84.

### Answer: 2.84

Expected answer: 71/25

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation 153 = 91 + 5 * s for s, we need to isolate s on one side of the equation.

Given equation: 153 = 91 + 5 * s

Step 1: Subtract 91 from both sides of the equation to isolate the term with s.
153 - 91 = 91 + 5 * s - 91
62 = 5 * s

Step 2: Divide both sides of the equation by 5 to get s alone.
62 / 5 = 5 * s / 5
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 Sonnet:

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

Given equation: 65 = (22 + (30 * g))

Step 1: Subtract 22 from both sides of the equation.
65 - 22 = (22 + (30 * g)) - 22
43 = 30 * g

Step 2: Divide both sides of the equation by 30.
43 / 30 = (30 * g) / 30
43/30 = g

Step 3: Evaluate the left-hand side.
43/30 = 1.43333...

Therefore, the value of g is approximately 1.43.

### Answer: 1.43

Expected answer: 43/30

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 96 = ((29 * f) + 10) for the value of f, we need to isolate f on one side of the equation.

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

Step 2: Divide both sides of the equation by 29 to isolate f.
86 / 29 = (29 * f) / 29
3 = f

Therefore, the value of f that satisfies the equation 96 = ((29 * f) + 10) is 3.

### Answer: 3

Expected answer: 86/29

Correct? No

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

Claude-3 Sonnet:

To solve the equation 80 = (19 + (14 * q)) for the variable q, we need to isolate q on one side of the equation.

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

Step 1: Remove the parentheses by distributing 14.
80 = 19 + 14q

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

Step 3: Divide both sides of the equation by 14.
61/14 = 14q/14
q = 61/14

Step 4: Simplify the fraction.
q = 4.357142857...

Therefore, the value of q that satisfies the equation 80 = (19 + (14 * q)) is approximately 4.357142857.

### Answer: 4.357142857

Expected answer: 61/14

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation for the variable 'm', we need to isolate 'm' on one side of the equation by performing inverse operations.

Given equation: 145 = 95 + 46 * m

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

Step 2: Divide both sides of the equation by 46 to find the value of 'm'.
50 / 46 = 46 * m / 46
m = 50 / 46

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 2.
m = (50 / 2) / (46 / 2)
m = 25 / 23

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

### Answer: m = 25 / 23

Expected answer: 25/23

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation for the value of 'i', we need to isolate 'i' on one side of the equation.

Given equation: 68 = 13 + 6 * i

Step 1: Subtract 13 from both sides of the equation.
68 - 13 = 13 + 6 * i - 13
55 = 6 * i

Step 2: Divide both sides of the equation by 6.
55 / 6 = 6 * i / 6
9.166666... = i

Therefore, the value of 'i' in the equation 68 = 13 + 6 * i is approximately 9.17.

### Answer: 9.17

Expected answer: 55/6

Correct? No

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

Claude-3 Sonnet:

To solve the equation for the value of h, we need to perform the following steps:

Step 1: Isolate the term containing h on one side of the equation.
25 = (74 * h) - 61
25 + 61 = (74 * h) - 61 + 61
86 = 74 * h

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

Step 3: Perform the division to find the value of h.
h = 86 / 74
h = 1.162162162...

Therefore, the value of h in the equation 25 = ((74 * h) - 61) is approximately 1.162162162.

### Answer: 1.162162162

Expected answer: 43/37

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 51 = ((6 * q) - 30) for the value of q, we need to perform the following steps:

Step 1: Isolate the term with the variable q on one side of the equation.
51 = (6 * q) - 30
51 + 30 = (6 * q) - 30 + 30
81 = 6 * q

Step 2: Divide both sides of the equation by 6 to isolate 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 Sonnet:

To find the value of r, we need to rearrange the equation and isolate r on one side.

Given equation: 38 = 81 - 36r

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

Step 2: Divide both sides by -36 to isolate r.
-43/-36 = -36r/-36
r = 43/36
r = 1.194444...

Therefore, the value of r in the linear equation 38 = 81 - 36r is approximately 1.19.

### Answer: 1.19

Expected answer: 43/36

Correct? No

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

Claude-3 Sonnet:

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

Given equation: 90 = (23 + (56 * a))

Step 1: Remove the parentheses by distributing the multiplication.
90 = 23 + 56a

Step 2: Subtract 23 from both sides of the equation.
90 - 23 = 56a
67 = 56a

Step 3: Divide both sides of the equation by 56 to isolate 'a'.
67/56 = 56a/56
a = 67/56
a = 1.196428571

Therefore, the value of 'a' that satisfies the equation 90 = (23 + (56 * a)) is approximately 1.196428571.

### Answer: 1.196428571

Expected answer: 67/56

Correct? No

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

Claude-3 Sonnet:

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.

Given equation: 81 = 13 + 30 * h

Step 1: Subtract 13 from both sides of the equation to isolate the term with the variable h.
81 - 13 = 13 + 30 * h - 13
68 = 30 * h

Step 2: Divide both sides of the equation by 30 to find the value of h.
68 / 30 = 30 * h / 30
h = 68 / 30
h = 2.267 (rounded to 3 decimal places)

Therefore, the value of the unknown variable h that satisfies the equation 81 = 13 + 30 * h is approximately 2.267.

### Answer: 2.267

Expected answer: 34/15

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation for the value of m, we need to isolate m on one side of the equation by performing inverse operations.

Given equation: 160 = ((62 * m) + 69)

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

Step 2: Divide both sides of the equation by 62 to get the value of m.
91 / 62 = 62 * m / 62
m = 91 / 62

Step 3: Evaluate the expression on the right-hand side.
m = 91 / 62
m = 1.4677419354838709677419354839 (approximately)

Therefore, the value of m that satisfies the given linear equation is approximately 1.47.

### Answer: 1.47

Expected answer: 91/62

Correct? No

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

Claude-3 Sonnet:

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

Given equation: 100 = 69 + 28 * q

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

Step 2: Divide both sides of the equation by 28.
31 / 28 = 28 * q / 28
q = 31 / 28

Therefore, the value of q is 31/28.

### Answer: 31/28

Expected answer: 31/28

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation for w, we need to isolate w on one side of the equation by performing inverse operations.

Given equation: 192 = ((98 * w) + 94)

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

Step 2: Divide both sides of the equation by 98 to find the value of w.
98 / 98 = w
w = 1

Therefore, the value of w in the given linear equation 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 Sonnet:

To solve the equation 40 = 93 - 33 * y for y, we need to perform the following steps:

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

Step 2: Divide both sides of the equation by -33 to get y alone.
-53/-33 = (-33 * y)/-33
y = 53/33

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 1.
y = 53/33
y = 1.6060606...

Therefore, the value of y that satisfies the equation 40 = 93 - 33 * y is approximately 1.61.

### Answer: 1.61

Expected answer: 53/33

Correct? No

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

Claude-3 Sonnet:

To solve for the unknown variable u in the linear equation 74 = ((48 * u) - 20), we need to isolate u on one side of the equation.

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

Step 1: Add 20 to both sides of the equation to eliminate the constant term on the right-hand side.
74 + 20 = (48 * u) - 20 + 20
94 = 48 * u

Step 2: Divide both sides of the equation by 48 to isolate u.
94 / 48 = (48 * u) / 48
u = 94 / 48
u = 1.958333...

Therefore, the value of the unknown variable u in the given linear equation is approximately 1.958333.

### Answer: 1.958333

Expected answer: 47/24

Correct? No

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

Claude-3 Sonnet:

To solve the equation for the variable f, we need to isolate f on one side of the equation by performing inverse operations.

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

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

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

Step 3: Evaluate the division to find the value of f.
f = 1.0348837209302326

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

### Answer: 1.0348837209302326

Expected answer: 89/86

Correct? No

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

Claude-3 Sonnet:

To solve the equation for c, we need to isolate c on one side of the equation.

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

Step 1: Subtract 36 from both sides of the equation.
122 - 36 = 36 + (56 * c) - 36
86 = 56 * c

Step 2: Divide both sides of the equation by 56.
86 / 56 = (56 * c) / 56
c = 86 / 56
c = 1.5357142857142856

Therefore, the value of c that satisfies the equation 122 = (36 + (56 * c)) is approximately 1.54.

### Answer: 1.54

Expected answer: 43/28

Correct? No

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

Claude-3 Sonnet:

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.

Given equation: 186 = 99 + 81 * q

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

Step 2: Divide both sides of the equation by 81 to find the value of q.
87 / 81 = 81 * q / 81
q = 87 / 81
q = 1.0740740740740742

Therefore, the value of q that satisfies the equation 186 = 99 + 81 * q is approximately 1.0740740740740742.

### Answer: 1.0740740740740742

Expected answer: 29/27

Correct? Yes

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

Claude-3 Sonnet:

To find the value of 'u' in the given equation, we need to isolate 'u' on one side of the equation.

Given equation: 120 = ((42 * u) + 77)

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

Step 2: Divide both sides of the equation by 42 to find the value of 'u'.
43 / 42 = (42 * u) / 42
u = 1.02380952380952

Therefore, the value of 'u' in the given equation is approximately 1.02.

### Answer: 1.02

Expected answer: 43/42

Correct? No

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

Claude-3 Sonnet:

To solve the equation for the value of j, we need to isolate j on one side of the equation.

Given equation: 103 = (52 + (6 * j))

Step 1: Subtract 52 from both sides of the equation.
103 - 52 = (52 + (6 * j)) - 52
51 = 6 * j

Step 2: Divide both sides of the equation by 6.
51 / 6 = (6 * j) / 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 Sonnet:

To solve the linear equation for the value of n, we need to perform the following steps:

Step 1: Simplify the right-hand side of the equation by performing the operations inside the parentheses.
56 = 82 - (4 × n)
56 = 82 - 4n

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

Step 3: Divide both sides of the equation by -4 to find the value of n.
-26/-4 = n
6.5 = n

Therefore, the value of n that satisfies the linear 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 Sonnet:

To solve the linear equation 77 = 14 + 60 * m for m, we need to isolate m on one side of the equation.

Step 1: Subtract 14 from both sides of the equation to get rid of the constant term on the right-hand side.
77 - 14 = 14 + 60 * m - 14
63 = 60 * m

Step 2: Divide both sides of the equation by 60 to isolate m.
63 / 60 = 60 * m / 60
m = 63 / 60
m = 1.05

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 Sonnet:

To solve the linear equation 31 = 17 + e for the variable e, we need to isolate e on one side of the equation by performing inverse operations.

Given equation: 31 = 17 + e

Step 1: Subtract 17 from both sides of the equation to isolate the variable term.
31 - 17 = 17 + e - 17
14 = e

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

### Answer: 14

Expected answer: 14

Correct? Yes

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

Claude-3 Sonnet:

To solve this equation for x, we need to isolate x on one side of the equation.

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

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

Step 2: Divide both sides of the equation by -15 to isolate x.
-79/-15 = -15x/-15
x = 79/15

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 1.
x = 79/15

Therefore, the value of x that solves the equation 2 = 81 - (15 * x) is 79/15.

### Answer: 79/15

Expected answer: 79/15

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation for the value of e, we need to isolate e on one side of the equation.

Given equation: 177 = 88 + 6 * e

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

Step 2: Divide both sides of the equation by 6 to isolate e.
89 / 6 = 6 * e / 6
e = 89 / 6
e = 14.83333...

Therefore, the value of e in the equation 177 = 88 + 6 * e is approximately 14.83.

### Answer: 14.83

Expected answer: 89/6

Correct? No

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

Claude-3 Sonnet:

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

Step 1: Subtract 15 from both sides of the equation to get rid of the constant term on the right side.
95 - 15 = 3*r + 15 - 15
80 = 3*r

Step 2: Divide both sides of the equation by 3 to isolate r.
80/3 = 3*r/3
r = 80/3

Step 3: Evaluate the expression on the right side.
r = 80/3
r = 26.67 (rounded to two decimal places)

Therefore, the value of r that satisfies the equation 95 = 3*r + 15 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 Sonnet:

To solve the linear equation for the value of v, we need to isolate v on one side of the equation.

Given equation: 154 = (70 + (31 * v))

Step 1: Remove the parentheses by distributing the 31.
154 = 70 + 31v

Step 2: Subtract 70 from both sides of the equation.
154 - 70 = 31v
84 = 31v

Step 3: Divide both sides of the equation by 31.
84/31 = 31v/31
2.7096774193548387 = v

Therefore, the value of v in the given linear equation is approximately 2.71.

### Answer: 2.71

Expected answer: 84/31

Correct? No

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

Claude-3 Sonnet:

To solve the equation for the value of r, we need to isolate r on one side of the equation.

Given equation: 179 = ((70 * r) + 87)

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

Step 2: Divide both sides of the equation by 70 to get the value of r.
92 / 70 = 70 * r / 70
r = 92 / 70
r = 1.314285714285714

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 Sonnet:

To solve the equation 93 = ((19 * r) + 2) for the value of r, we need to perform the following steps:

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

Step 2: Divide both sides of the equation by 19 to find the value of r.
91 / 19 = 19 * r / 19
r = 4.79

Therefore, the value of r that satisfies the equation 93 = ((19 * r) + 2) is 4.79.

### Answer: 4.79

Expected answer: 91/19

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 20 = (67 - (37 * z)) for the value of z, we need to perform the following steps:

Step 1: Simplify the right-hand side of the equation by performing the multiplication first.
20 = (67 - 37z)

Step 2: Subtract 67 from both sides of the equation to isolate the term with z.
20 - 67 = 67 - 37z
-47 = -37z

Step 3: Divide both sides of the equation by -37 to find the value of z.
-47/-37 = -37z/-37
z = 47/37

Therefore, the value of z that satisfies the linear equation 20 = (67 - (37 * z)) is z = 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 Sonnet:

To solve the linear equation 65 = ((25 * m) + 15) for m, we need to isolate the variable m on one side of the equation.

Step 1: Subtract 15 from both sides of the equation to remove the constant term on the right-hand side.
65 - 15 = (25 * m) + 15 - 15
50 = 25 * m

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

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

### Answer: 2

Expected answer: 2

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation 79 = ((6 * g) + 19) for g, we need to isolate g on one side of the equation.

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

Step 2: Divide both sides of the equation by 6 to isolate g.
60 / 6 = 6 * g / 6
10 = g

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

### Answer: 10

Expected answer: 10

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation for the variable 'l', we need to isolate 'l' on one side of the equation by performing inverse operations.

Given equation: 30 = ((56 * l) - 45)

Step 1: Add 45 to both sides of the equation to eliminate the subtraction.
30 + 45 = (56 * l) - 45 + 45
75 = 56 * l

Step 2: Divide both sides of the equation by 56 to isolate 'l'.
75 / 56 = (56 * l) / 56
(75 / 56) = l

Step 3: Simplify the fraction on the left-hand side.
(75 / 56) = (25 * 3) / (8 * 7)
(75 / 56) = (25 / 8) * (3 / 7)
(75 / 56) = 3.125 * (3 / 7)
(75 / 56) = 10.71428571

Therefore, the value of 'l' is approximately 10.71428571.

### Answer: 10.71428571

Expected answer: 75/56

Correct? No

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

Claude-3 Sonnet:

To solve the equation 57 = ((11 * j) + 4) for the value of j, we need to perform the following steps:

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

Step 2: Divide both sides of the equation by 11 to find the value of j.
53 / 11 = 11 * j / 11
j = 53 / 11
j = 4.818181818181818

Therefore, the value of j in the equation 57 = ((11 * j) + 4) is approximately 4.818181818181818.

### Answer: 4.818181818181818

Expected answer: 53/11

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation 36 = 34 * f - 56 for the value of f, we need to perform the following steps:

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

Step 2: Divide both sides of the equation by 34 to get the value of f.
92 / 34 = 34 * f / 34
2.7058823529411766 = f

Therefore, the value of f in the equation 36 = 34 * f - 56 is approximately 2.71.

### Answer: 2.71

Expected answer: 46/17

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 56 = (70 * u) - 43 for the value of u, we need to perform the following steps:

Step 1: Isolate the term containing the variable u on one side of the equation.
56 = (70 * u) - 43
56 + 43 = (70 * u) - 43 + 43
99 = 70 * u

Step 2: Divide both sides of the equation by 70 to get the value of u.
99 / 70 = 70 * u / 70
u = 99 / 70
u = 1.414285714285714

Therefore, the value of u in the linear equation 56 = (70 * u) - 43 is approximately 1.414285714285714.

### Answer: 1.414285714285714

Expected answer: 99/70

Correct? No

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

Claude-3 Sonnet:

To solve the equation 67 = 21 + 9*x for the variable x, we need to isolate x on one side of the equation.

Given equation: 67 = 21 + 9*x

Step 1: Subtract 21 from both sides of the equation to isolate the term with x.
67 - 21 = 21 + 9*x - 21
46 = 9*x

Step 2: Divide both sides of the equation by 9 to get x alone.
46/9 = 9*x/9
x = 46/9

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.
x = (46/2) / (9/2)
x = 23/4.5
x = 5.11 (approximately)

Therefore, the value of x that satisfies the equation 67 = 21 + 9*x is approximately 5.11.

### Answer: 5.11

Expected answer: 46/9

Correct? No

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

Claude-3 Sonnet:

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 equation: 75 = (58 + 16 * i)

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

Step 2: Divide both sides of the equation by 16 to find the value of i.
17 / 16 = 16 * i / 16
i = 17 / 16
i = 1.0625

Therefore, the value of the unknown variable i in the equation 75 = (58 + 16 * 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 Sonnet:

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

Given equation: 111 = (54 + (39 * x))

Step 1: Remove the parentheses by distributing 39.
111 = 54 + 39x

Step 2: Subtract 54 from both sides of the equation.
111 - 54 = 39x
57 = 39x

Step 3: Divide both sides of the equation by 39.
57/39 = 39x/39
1.46... = x

Therefore, the value of x that satisfies the equation 111 = (54 + (39 * x)) is approximately 1.46.

### Answer: 1.46

Expected answer: 19/13

Correct? No

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

Claude-3 Sonnet:

To solve the equation for the value of 'o', we need to isolate 'o' on one side of the equation.

Given equation: 155 = ((26 * o) + 68)

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

Step 2: Divide both sides of the equation by 26 to find the value of 'o'.
87 / 26 = 26 * o / 26
o = 87 / 26
o = 3.346153846153846

Therefore, the value of 'o' in the given equation is approximately 3.346.

### Answer: 3.346

Expected answer: 87/26

Correct? No

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

Claude-3 Sonnet:

To solve for p in the equation 7 = ((12 * p) - 17), we need to perform the following steps:

Step 1: Isolate the term with p by adding 17 to both sides of the equation.
7 + 17 = ((12 * p) - 17) + 17
24 = 12 * p

Step 2: Divide both sides of the equation by 12 to get p alone.
24/12 = 12 * p / 12
2 = p

Therefore, the value of p that satisfies the equation 7 = ((12 * p) - 17) is 2.

### Answer: 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 Sonnet:

To solve this problem, we need to isolate the variable 'b' on one side of the equation.

Given equation: 163 = 93 + 55 * b

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

Step 2: Divide both sides of the equation by 55.
70 / 55 = 55 * b / 55
b = 1.27272727...

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 Sonnet:

To solve the linear equation 62 = (u - 26) for the value of u, we need to perform the following steps:

Step 1: Isolate the variable term (u - 26) on one side of the equation.
62 = (u - 26)

Step 2: Add 26 to both sides of the equation to eliminate the constant term on the right side.
62 + 26 = (u - 26) + 26
88 = u

Therefore, the value of u that satisfies the equation 62 = (u - 26) is 88.

### Answer: 88

Expected answer: 88

Correct? Yes

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

Claude-3 Sonnet:

To solve the equation for the variable a, we need to isolate a on one side of the equation.

Given equation: 179 = ((63 * a) + 93)

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

Step 2: Divide both sides of the equation by 63 to get the value of a.
86 / 63 = 63 * a / 63
a = 86 / 63
a = 1.365079365079365

Therefore, the value of a that satisfies the equation 179 = ((63 * a) + 93) is approximately 1.365079365079365.

### Answer: 1.365079365079365

Expected answer: 86/63

Correct? No

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

Claude-3 Sonnet:

To find the value of c in the equation 51 = ((27 * c) - 11), we need to perform the following steps:

Step 1: Simplify the right-hand side of the equation by multiplying 27 by c.
51 = (27c - 11)

Step 2: Add 11 to both sides of the equation to isolate 27c.
51 + 11 = 27c - 11 + 11
62 = 27c

Step 3: Divide both sides of the equation by 27 to find the value of c.
62/27 = 27c/27
c = 2.296296296...

Therefore, the value of c in the equation 51 = ((27 * c) - 11) is approximately 2.296.

### Answer: 2.296

Expected answer: 62/27

Correct? No

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

Claude-3 Sonnet:

To solve the equation 19 = ((28 * d) - 18) for d, we need to perform the following steps:

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

Step 2: Divide both sides of the equation by 28 to get d alone.
37 / 28 = (28 * d) / 28
37 / 28 = d

Step 3: Simplify the fraction on the left side.
37 / 28 = 1 + 9/28

Therefore, the solution for d is:
d = 1 + 9/28

### Answer: 1 + 9/28

Expected answer: 37/28

Correct? Yes

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

Claude-3 Sonnet:

To solve the linear equation for the value of e, we need to isolate e on one side of the equation.

Given equation: 159 = ((47 * e) + 62)

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

Step 2: Divide both sides of the equation by 47 to get the value of e.
97 / 47 = 47 * e / 47
e = 97 / 47

Step 3: Evaluate the expression on the right-hand side.
e = 97 / 47
e = 2.063829787234043

Therefore, the value of e that satisfies the given linear equation is approximately 2.064.

### Answer: 2.064

Expected answer: 97/47

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation for the variable g, we need to isolate g on one side of the equation.

Given equation: 145 = (50 + (91 * g))

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

Step 2: Divide both sides of the equation by 91 to get the value of g.
95 / 91 = (91 * g) / 91
g = 1.044

Therefore, the value of g that satisfies the given linear equation is 1.044.

### Answer: 1.044

Expected answer: 95/91

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation for the value of l, we need to isolate l on one side of the equation.

Given equation: 123 = ((44 * l) + 73)

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

Step 2: Divide both sides of the equation by 44 to get the value of l.
50 / 44 = 44 * l / 44
l = 50 / 44
l = 25 / 22

Therefore, the value of l in the given linear equation is 25/22 or approximately 1.136.

### Answer: 25/22

Expected answer: 25/22

Correct? Yes

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

Claude-3 Sonnet:

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

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

Step 2: Divide both sides of the equation by 19.
90/19 = (19 * q)/19
4.7368421... = q

Therefore, the solution to the equation 165 = ((19 * q) + 75) is q = 4.7368421...

### Answer: 4.7368421...

Expected answer: 90/19

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 149 = ((18 * g) + 62) for the value of g, we need to perform the following steps:

Step 1: Isolate the term containing the variable g on one side of the equation.
149 = (18 * g) + 62
149 - 62 = (18 * g) + 62 - 62
87 = 18 * g

Step 2: Divide both sides of the equation by 18 to find the value of g.
87 / 18 = 18 * g / 18
g = 87 / 18
g = 4.83 (rounded to two decimal places)

Therefore, the value of g in the equation 149 = ((18 * g) + 62) is approximately 4.83.

### Answer: 4.83

Expected answer: 29/6

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 84 = 20 * d + 21 for the variable d, we need to isolate d on one side of the equation by performing inverse operations.

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

Step 2: Divide both sides of the equation by 20 to isolate d.
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 Sonnet:

To solve the equation for the value of g, we need to isolate g on one side of the equation.

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

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

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

Step 3: Evaluate the expression on the left side.
11/6 = 1.833...

Therefore, the value of g is approximately 1.833.

### Answer: 1.833

Expected answer: 11/6

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation for the unknown variable v, we need to isolate v on one side of the equation by performing inverse operations.

Given equation: 126 = ((21 * v) + 76)

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

Step 2: Divide both sides of the equation by 21 to get v alone.
50 / 21 = (21 * v) / 21
v = 50 / 21

Step 3: Evaluate the expression on the right-hand side.
v = 50 / 21
v = 2.38095238095238

Therefore, the value of the unknown variable v is approximately 2.38.

### Answer: 2.38

Expected answer: 50/21

Correct? No

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

Claude-3 Sonnet:

To solve the linear equation 74 = ((91 * g) - 24) for g, we need to perform the following steps:

Step 1: Isolate the term containing the variable g on one side of the equation.
74 + 24 = (91 * g) - 24 + 24
98 = 91 * g

Step 2: Divide both sides of the equation by 91 to get the value of g.
98 / 91 = 91 * g / 91
g = 98 / 91

Therefore, the solution to the linear equation 74 = ((91 * g) - 24) is g = 98 / 91.

### Answer: 98/91

Expected answer: 14/13

Correct? Yes