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

Gemini-1.5 Pro:

Reasoning: First, subtract 92 from both sides of the equation: 122 - 92 = 92 + 28 * u - 92, which simplifies to 30 = 28 * u
Then, divide both sides of the equation by 28: 30 / 28 = 28 * u / 28, which simplifies to 15/14 = u
### Answer: u = 15/14 

Expected answer: 15/14

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, add 34 to both sides of the equation: 42 + 34 = (35 * i) - 34 + 34 which simplifies to 76 = (35 * i).
Next, divide both sides of the equation by 35: 76 / 35 = (35 * i) / 35 which simplifies to 76/35 = i.

### Answer: i = 76/35

Expected answer: 76/35

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. **Isolate the term with 'r':** Subtract 41 from both sides of the equation: 
   94 - 41 = 41 + 6r - 41
   53 = 6r

2. **Solve for 'r':** Divide both sides of the equation by 6:
   53 / 6 = 6r / 6

3. **Simplify:** 
   r = 8.83 (rounded to two decimal places)

### Answer: r = 8.83 

Expected answer: 53/6

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
Step 1: Subtract 94 from both sides of the equation: 158 - 94 = ((19 * i) + 94) - 94 which simplifies to 64 = (19 * i)
Step 2: Divide both sides of the equation by 19: 64/19 = (19 * i)/19 which simplifies to i = 64/19
Step 3: Calculate the division: i = 3.37 (rounding to two decimal places) 
### Answer: i = 3.37 

Expected answer: 64/19

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 54 from both sides of the equation: 134 - 54 = (30 * q) + 54 - 54, which simplifies to 80 = 30 * q.

2. Divide both sides of the equation by 30: 80 / 30 = (30 * q) / 30, which simplifies to 8/3 = q.

### Answer: q = 8/3 

Expected answer: 8/3

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To isolate y, subtract 27 from both sides of the equation.
94 - 27 = (27 + y) - 27
This simplifies to: 
67 = y 
### Answer: y = 67 

Expected answer: 67

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, add 70 to both sides of the equation to isolate the term with h: 9 + 70 = ((23 * h) - 70) + 70, which simplifies to 79 = 23 * h.
Then, divide both sides of the equation by 23 to solve for h: 79 / 23 = (23 * h) / 23.

### Answer: h = 79/23

Expected answer: 79/23

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, subtract 26 from both sides of the equation to isolate the term with t:
92 - 26 = 33 * t + 26 - 26
This simplifies to:
66 = 33 * t

Next, divide both sides of the equation by 33 to solve for t:
66 / 33 = (33 * t) / 33
This gives us:
2 = t

### Answer: t = 2 

Expected answer: 2

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 29 from both sides of the equation: 123 - 29 = ((15 * e) + 29) - 29 which simplifies to 94 = (15 * e)
2. Divide both sides of the equation by 15:  94 / 15 = (15 * e) / 15 which simplifies to e = 6.27 when rounded to the nearest hundredth. 
### Answer: e = 6.27

Expected answer: 94/15

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, add 80 to both sides of the equation: 16 + 80 = (75 * k) - 80 + 80, which simplifies to 96 = 75 * k.

Then, divide both sides of the equation by 75: 96 / 75 = (75 * k) / 75, which simplifies to 1.28 = k

### Answer: k = 1.28 

Expected answer: 32/25

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, subtract 89 from both sides: 131 - 89 = (5 * q) + 89 - 89 which simplifies to 42 = (5 * q)
Then, divide both sides by 5: 42 / 5 = (5 * q) / 5 which simplifies to 8.4 = q

### Answer: q = 8.4 

Expected answer: 42/5

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 56 from both sides of the equation: 147 - 56 = ((38 * p) + 56) - 56, which simplifies to 91 = 38 * p.
2. Divide both sides of the equation by 38: 91 / 38 = (38 * p) / 38, which simplifies to p = 91/38.
3. Calculate the division: p = 2.395 (rounded to three decimal places).

### Answer: p = 2.395 

Expected answer: 91/38

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 23 from both sides of the equation:  76 - 23 = 42 * j + 23 - 23, which simplifies to 53 = 42 * j
2. Divide both sides of the equation by 42: 53 / 42 = (42 * j) / 42, which simplifies to 53/42 = j
3. Calculate the result: 53 / 42 = 1.26 

### Answer: j = 1.26

Expected answer: 53/42

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
 
 1. **Isolate the term with 'l':** Subtract 43 from both sides of the equation: 
    138 - 43 = 43 + 25 * l - 43
    95 = 25 * l
 
 2. **Solve for 'l':** Divide both sides of the equation by 25:
    95 / 25 = (25 * l) / 25
    3.8 = l

### Answer: l = 3.8 

Expected answer: 19/5

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 35 from both sides of the equation: 80 - 35 = ((24 * w) + 35) - 35 which simplifies to 45 = 24 * w
2. Divide both sides of the equation by 24 to isolate w:  45 / 24 = (24 * w) / 24 which simplifies to 1.875 = w
### Answer: w = 1.875

Expected answer: 15/8

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
 1. First, calculate the value inside the parentheses: 14 * x = 14x
 2. Rewrite the equation with the result: 77 = 33 + 14x
 3. Isolate the x term by subtracting 33 from both sides: 77 - 33 = 33 + 14x - 33. This simplifies to 44 = 14x.
 4. Solve for x by dividing both sides by 14: 44 / 14 = 14x / 14.
 5. This gives us x = 22/7

### Answer: 22/7 

Expected answer: 22/7

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. First, we simplify the equation by subtracting 12 from both sides: 
   110 - 12 = 12 + 88 * y - 12
   98 = 88 * y

2. Next, we isolate y by dividing both sides by 88:
   98 / 88 = (88 * y) / 88
   1.1136 = y

### Answer: y = 1.1136 (rounded to four decimal places)

Expected answer: 49/44

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 80 from both sides of the equation to isolate the term with 's': 
   179 - 80 = 82 * s + 80 - 80
   99 = 82 * s

2. Divide both sides of the equation by 82 to solve for 's':
   99 / 82 = (82 * s) / 82
   99/82 = s

3. Simplify the fraction:
    s = 1.21 (rounded to two decimal places)

### Answer: s = 1.21 

Expected answer: 99/82

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, subtract 66 from both sides of the equation to isolate the term with m: 129 - 66 = 26 * m + 66 - 66, which simplifies to 63 = 26 * m
Then, divide both sides of the equation by 26 to solve for m: 63 / 26 = 26 * m / 26, which simplifies to 63/26 = m

### Answer: m = 63/26

Expected answer: 63/26

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Add 17 to both sides of the equation: 82 + 17 = ((27 * q) - 17) + 17, which simplifies to 99 = (27 * q).
2. Divide both sides of the equation by 27:  99 / 27 = (27 * q) / 27.
3. This simplifies to q = 3.66667, which rounds to 3.67

### Answer: q = 3.67

Expected answer: 11/3

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Start by simplifying inside the parentheses: 141 = (64 + 22k)
2. Subtract 64 from both sides of the equation: 141 - 64 = 64 + 22k - 64, which simplifies to 77 = 22k
3. Divide both sides of the equation by 22: 77 / 22 = 22k / 22 
4. Simplify to get the value of k:  3.5 = k

### Answer: k = 3.5 

Expected answer: 7/2

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 91 from both sides of the equation to isolate the term with 'v': 175 - 91 = 91 + 45v - 91, which simplifies to 84 = 45v 
2. Divide both sides of the equation by 45 to solve for 'v': 84 / 45 = 45v / 45
3. Simplify to get the value of 'v': v = 1.87

### Answer: v = 1.87 

Expected answer: 28/15

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
1. Add 18 to both sides of the equation: 50 + 18 = (63 * k) - 18 + 18, which simplifies to 68 = (63 * k).
2. Divide both sides of the equation by 63: 68 / 63 = (63 * k) / 63.
3. This simplifies to k = 68/63.

### Answer: k = 68/63 

Expected answer: 68/63

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
 First, we add 10 to both sides of the equation: 65 + 10 = ((8 * l) - 10) + 10, which simplifies to 75 = 8 * l
 Next, we divide both sides of the equation by 8:  75 / 8 = (8 * l) / 8.

### Answer: l = 9.375 

Expected answer: 75/8

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, add 34 to both sides of the equation: 5 + 34 = ((10 * u) - 34) + 34 which simplifies to 39 = (10 * u)
Then, divide both sides of the equation by 10:  39 / 10 = (10 * u) / 10 which simplifies to 3.9 = u
### Answer: u = 3.9 

Expected answer: 39/10

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 61 from both sides of the equation to isolate the term with 'a':  91 - 61 = 9 * a + 61 - 61. This simplifies to 30 = 9 * a.
2. Divide both sides of the equation by 9 to solve for 'a': 30 / 9 = (9 * a) / 9.
3. Simplify to get the value of 'a': a = 10/3. 
### Answer: a = 10/3 

Expected answer: 10/3

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 61 from both sides of the equation to isolate the term with i: 157 - 61 = 53 * i + 61 - 61. This simplifies to 96 = 53 * i.
2. Divide both sides of the equation by 53 to solve for i: 96 / 53 = (53 * i) / 53.

### Answer: i = 96/53 

Expected answer: 96/53

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 14 from both sides of the equation to isolate the term with q: 71 - 14 = ((24 * q) + 14) - 14, which simplifies to 57 = 24 * q
2. Divide both sides of the equation by 24 to solve for q: 57 / 24 = (24 * q) / 24.
3. This simplifies to q = 2.375

### Answer: q = 2.375 

Expected answer: 19/8

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 96 from both sides of the equation: 163 - 96 = 96 + 14i - 96 which simplifies to 67 = 14i.
2. Divide both sides of the equation by 14: 67 / 14 = 14i / 14, which simplifies to i = 4.79 (rounded to the nearest hundredth). 
### Answer: i = 4.79

Expected answer: 67/14

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Add 23 to both sides of the equation to isolate the term with 'e': 
   59 + 23 = (70 * e) - 23 + 23
   82 = 70 * e 

2. Divide both sides of the equation by 70 to isolate 'e':
   82 / 70 = (70 * e) / 70

3. Simplify:
   e = 82 / 70 
   e = 1.17 (rounded to two decimal places) 

### Answer: e = 1.17 

Expected answer: 41/35

Correct? No

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

Gemini-1.5 Pro:

To solve for *o* in the equation 147 = 36 * *o* + 74, we follow these steps:

1. **Isolate the term with *o*:** 
   Subtract 74 from both sides of the equation:
   147 - 74 = 36 * *o* + 74 - 74
   This simplifies to: 73 = 36 * *o*

2. **Solve for *o*:**
   Divide both sides of the equation by 36:
   73 / 36 = (36 * *o*) / 36
   This simplifies to:  73/36 = *o*

### Answer: o = 73/36 

Expected answer: 73/36

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 93 from each side: 71 - 93 = 93 - (13 * d) - 93 which simplifies to -22 = - (13 * d)
2. Multiply each side by -1: (-22) * (-1) = -(13 * d) * (-1) which simplifies to 22 = 13 * d
3. Divide each side by 13: 22 / 13 = (13 * d) / 13 which simplifies to 22/13 = d
### Answer: 22/13 

Expected answer: 22/13

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
First, subtract 64 from both sides: 118 - 64 = 64 + 6 * n - 64, which simplifies to 54 = 6 * n
Then, divide both sides by 6: 54 / 6 = 6 * n / 6, which simplifies to 9 = n.
### Answer: n = 9 

Expected answer: 9

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. **Isolate the term with 'd':** Add 7 to both sides of the equation: 
   61 + 7 = (5 * d) - 7 + 7
   68 = (5 * d)

2. **Solve for 'd':** Divide both sides of the equation by 5:
   68 / 5 = (5 * d) / 5 
   13.6 = d

### Answer: d = 13.6 

Expected answer: 68/5

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Add 18 to both sides of the equation: 79 + 18 = (8 * z) - 18 + 18 which simplifies to 97 = (8 * z)
2. Divide both sides of the equation by 8:  97 / 8 = (8 * z) / 8
3. This simplifies to z = 12.125

### Answer: z = 12.125 

Expected answer: 97/8

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 63 from both sides:  129 - 63 = ((2 * z) + 63) - 63 which simplifies to 66 = 2 * z
2. Divide both sides by 2: 66 / 2 = (2 * z) / 2 which simplifies to 33 = z

### Answer: z = 33 

Expected answer: 33

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. First, we simplify inside the parenthesis: 127 = 29 + 32e 
2. Next, we subtract 29 from both sides: 98 = 32e
3. Finally, we divide both sides by 32 to isolate e: e = 98 / 32 = 3.0625

### Answer: e = 3.0625 

Expected answer: 49/16

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, add 35 to both sides of the equation: 30 + 35 = (50 * x) - 35 + 35 which simplifies to 65 = (50 * x).
Next, divide both sides of the equation by 50: 65 / 50 = (50 * x) / 50.
This simplifies to 1.3 = x.

### Answer: x = 1.3

Expected answer: 13/10

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
First subtract 9 from both sides: 66 - 9 = 9 + 10 * x - 9 which becomes 57 = 10 * x
Then, divide both sides by 10: 57 / 10 = 10 * x / 10 which becomes 5.7 = x
### Answer: x = 5.7 

Expected answer: 57/10

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 51 from both sides of the equation: 103 - 51 = ((38 * a) + 51) - 51 which becomes  52 = 38 * a 
2. Divide both sides of the equation by 38: 52 / 38 = (38 * a) / 38 which becomes 1.37 = a.

### Answer: a = 1.37 

Expected answer: 26/19

Correct? No

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

Gemini-1.5 Pro:

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

2. Divide both sides of the equation by 28 to solve for f:
    97 / 28 = (28 * f) / 28
    3.4643 ≈ f

### Answer: f ≈ 3.4643 

Expected answer: 97/28

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 63 from both sides: 12-63 = 63 - 50*u - 63, which simplifies to -51 = -50*u.
2. Divide both sides by -50: -51 / -50 = -50*u / -50, which simplifies to 1.02 = u

### Answer: u = 1.02 

Expected answer: 51/50

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 42 from both sides of the equation to isolate the term with 'b': 60 - 42 = 42 + (10 * b) - 42, which simplifies to 18 = 10 * b
2. Divide both sides of the equation by 10 to solve for 'b': 18 / 10 = (10 * b) / 10
3. This simplifies to b = 1.8

### Answer: b = 1.8 

Expected answer: 9/5

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
 1. Subtract 13 from both sides: 84 - 13 = ((25 * j) + 13) - 13 which simplifies to 71 = 25 * j
 2. Divide both sides by 25: 71 / 25 = (25 * j) / 25.

### Answer: j = 2.84 

Expected answer: 71/25

Correct? Yes

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

Gemini-1.5 Pro:

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

2. Divide both sides of the equation by 5 to solve for s:
   62 / 5 = 5s / 5
   12.4 = s
### Answer: s = 12.4 

Expected answer: 62/5

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. First, we simplify inside the parentheses: 65 = (22 + 30g)
2. Next, we isolate the term with 'g' by subtracting 22 from both sides: 65 - 22 = 30g, which simplifies to 43 = 30g
3. Finally, we solve for 'g' by dividing both sides by 30: 43 / 30 = g

### Answer: g = 43/30 

Expected answer: 43/30

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 10 from both sides of the equation: 
   96 - 10 = ((29 * f) + 10) - 10
   This simplifies to: 86 = 29 * f
2. Divide both sides of the equation by 29 to isolate f:
   86 / 29 = (29 * f) / 29
   This simplifies to: 3 = f 

### Answer: f = 3 

Expected answer: 86/29

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. First, we simplify inside the parentheses: 80 = (19 + 14q)
2. Next, subtract 19 from both sides of the equation: 80-19 = (19 + 14q) - 19 which simplifies to 61 = 14q
3. Finally, divide both sides of the equation by 14:  61/14 = (14q)/14. This gives us q = 61/14. 

### Answer: q = 61/14

Expected answer: 61/14

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 95 from both sides of the equation: 145 - 95 = 95 + 46 * m - 95, which simplifies to 50 = 46 * m
2. Divide both sides of the equation by 46:  50 / 46 = 46 * m / 46, which simplifies to  m = 50/46
3. Simplify the fraction: m = 25/23

### Answer: m = 25/23 

Expected answer: 25/23

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
 1. Subtract 13 from each side:  68 - 13 = 13 + 6*i - 13 which simplifies to 55 = 6*i
 2. Divide both sides by 6: 55 / 6 = 6*i / 6  which simplifies to  i = 9.16666666667

### Answer: i = 9.16666666667 

Expected answer: 55/6

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, add 61 to both sides of the equation to isolate the term with h: 25 + 61 = ((74 * h) - 61) + 61. That simplifies to 86 = 74 * h
Next, divide both sides of the equation by 74 to isolate h:  86 / 74 = (74 * h) / 74. This gives us 1.162 = h

### Answer: h = 1.162 

Expected answer: 43/37

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Add 30 to both sides of the equation: 51 + 30 = ((6 * q) - 30) + 30 which simplifies to 81 = (6 * q)
2. Divide both sides of the equation by 6: 81 / 6 = (6 * q) / 6 which simplifies to q = 13.5
### Answer: q = 13.5 

Expected answer: 27/2

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 81 from both sides: 38-81 = 81 - 36 * r - 81, which simplifies to -43 = -36 * r
2. Divide both sides by -36: -43/-36 = -36 * r / -36, which simplifies to r = 1.1944

### Answer: r = 1.1944 

Expected answer: 43/36

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
1. **Simplify inside the parentheses:** 56 * a 
2. **Isolate the term with 'a':** Subtract 23 from both sides: 90 - 23 = (23 + (56 * a)) - 23  which simplifies to 67 = 56 * a
3. **Solve for 'a':** Divide both sides by 56:  67 / 56 = (56 * a) / 56

### Answer: a = 67/56 

Expected answer: 67/56

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
 1. Subtract 13 from both sides of the equation to isolate the term with h: 81 - 13 = 13 + 30 * h - 13, which simplifies to 68 = 30 * h
 2. Divide both sides of the equation by 30 to isolate h: 68 / 30 = 30 * h / 30, which simplifies to 2.2667 = h
 3. Round to the nearest thousandth: h ≈ 2.267
### Answer: h ≈ 2.267

Expected answer: 34/15

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 69 from both sides of the equation: 160 - 69 = ((62 * m) + 69) - 69 which becomes 91 = 62 * m
2. Divide both sides of the equation by 62: 91 / 62 = (62 * m) / 62
This simplifies to  m = 91 / 62

### Answer: m = 91/62 

Expected answer: 91/62

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:  First, we simplify the right side of the equation: 100 = 69 + 28q 
Then, we subtract 69 from both sides: 100 - 69 = 69 - 69 + 28q, which simplifies to  31 = 28q.
Next, we divide both sides of the equation by 28: 31 / 28 = 28q / 28
This gives us the value of q: q = 31/28 
### Answer: q = 31/28

Expected answer: 31/28

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
 1. Subtract 94 from both sides: 192 - 94 = ((98 * w) + 94) - 94 which simplifies to 98 = 98 * w
 2. Divide both sides by 98: 98 / 98 = (98 * w) / 98 which simplifies to 1 = w 
### Answer: w = 1 

Expected answer: 1

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. **Isolate the term with 'y':** Subtract 93 from both sides of the equation:
   40 - 93 = 93 - 33y - 93
   -53 = -33y

2. **Solve for 'y':** Divide both sides by -33:
   -53 / -33 = -33y / -33
   1.606 = y 

### Answer: y = 1.606 

Expected answer: 53/33

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Add 20 to both sides of the equation:  74 + 20 = ((48 * u) - 20) + 20 which simplifies to 94 = (48 * u)
2. Divide both sides of the equation by 48: 94 / 48 = (48 * u) / 48
3. This simplifies to u = 1.958333

### Answer: u = 1.958333

Expected answer: 47/24

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, add 76 to both sides of the equation: 13 + 76 = ((86 * f) - 76) + 76, which simplifies to 89 = 86 * f
Then, divide both sides of the equation by 86: 89 / 86 = (86 * f) / 86, which simplifies to 89/86 = f

### Answer: f = 89/86 

Expected answer: 89/86

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. First, we simplify inside the parentheses: 122 = (36 + (56 * c)) = 122 = 36 + 56c
2. Then, we subtract 36 from both sides of the equation: 122 - 36 = 36 + 56c - 36 
3. This simplifies to: 86 = 56c
4. Finally, we divide both sides by 56 to isolate c: 86 / 56 = 56c / 56
5. This gives us the solution: c = 1.536 (rounded to three decimal places)

### Answer: c = 1.536 

Expected answer: 43/28

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To solve for *q*, we'll follow these steps:

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

2. **Solve for *q*:**
   Divide both sides of the equation by 81:
   87 / 81 = 81*q / 81

   This simplifies to: q = 29/27

### Answer: q = 29/27 

Expected answer: 29/27

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 77 from both sides: 120 - 77 = ((42 * u) + 77) - 77 which simplifies to 43 = 42 * u
2. Divide both sides by 42 to isolate 'u':  43 / 42 = (42 * u) / 42
3. This gives us: u = 43/42

### Answer: u = 43/42 

Expected answer: 43/42

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. First, we simplify the expression inside the parenthesis: 52 + (6 * j) 
2. To isolate j, subtract 52 from both sides: 103 - 52 = (52 + (6 * j)) - 52 which becomes 51 = 6 * j
3. Divide both sides by 6 to solve for j: 51 / 6 = (6 * j) / 6
4. This gives us the value of j: j = 8.5

### Answer: j = 8.5 

Expected answer: 17/2

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. First, simplify inside the parentheses: 82 - (4 * n) = 82 - 4n
2. Rewrite the equation: 56 = 82 - 4n
3. Subtract 82 from both sides: 56 - 82 = 82 - 4n - 82 which simplifies to -26 = -4n
4. Divide both sides by -4: -26 / -4 = -4n / -4
5. Simplify for the answer: 6.5 = n

### Answer: n = 6.5 

Expected answer: 13/2

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 14 from both sides of the equation:  77 - 14 = 14 + 60 * m - 14, which simplifies to 63 = 60 * m.
2. Divide both sides of the equation by 60: 63 / 60 = 60 * m / 60.
3. This simplifies to 1.05 = m

### Answer: m = 1.05

Expected answer: 21/20

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:  Subtract 17 from both sides of the equation to isolate the variable 'e'. 
 
 31-17 = 17 - 17 + e
 
 14 = e
 
 This gives us 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)

Gemini-1.5 Pro:

Reasoning: 
First, isolate the term with x: 15 * x = 81 - 2 = 79
Then, solve for x: x = 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.

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 88 from both sides: 177 - 88 = 88 + 6 * e - 88 --> 89 = 6 * e
2. Divide both sides by 6: 89 / 6 = 6 * e / 6 --> e = 14.83

### Answer: e = 14.83

Expected answer: 89/6

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 15 from both sides of the equation: 95 - 15 = 3*r + 15 - 15, which simplifies to 80 = 3*r
2. Divide both sides of the equation by 3: 80 / 3 = 3*r / 3
3. This simplifies to r = 26.67 (rounded to two decimal places)

### Answer: r = 26.67 

Expected answer: 80/3

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
 1. **Simplify inside the parentheses:** 154 = (70 + 31v)
 2. **Subtract 70 from both sides:** 154 - 70 = (70 + 31v) - 70  which simplifies to 84 = 31v
 3. **Divide both sides by 31:** 84 / 31 = 31v / 31 which simplifies to  2.71 = v

### Answer: v = 2.71 

Expected answer: 84/31

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, subtract 87 from both sides: 179 - 87 = ((70 * r) + 87) - 87 which simplifies to 92 = 70 * r
Then, divide both sides by 70:  92 / 70 = (70 * r) / 70 which simplifies to r = 1.31
### Answer: r = 1.31

Expected answer: 46/35

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 2 from both sides of the equation: 93 - 2 = ((19 * r) + 2) - 2. This simplifies to 91 = 19 * r.
2. Divide both sides of the equation by 19: 91 / 19 = (19 * r) / 19. This gives us  r = 91 / 19
3. Calculate the result: r = 4.79

### Answer: r = 4.79

Expected answer: 91/19

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Distribute the -1 inside the parentheses:  20 = 67 - 37z
2. Subtract 67 from both sides of the equation: 20 - 67 = -37z.  This simplifies to -47 = -37z
3. Divide both sides of the equation by -37: -47 / -37 = z
4. Simplify: z = 1.27

### Answer: z = 1.27

Expected answer: 47/37

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 15 from both sides of the equation: 65 - 15 = ((25 * m) + 15) - 15, which simplifies to 50 = 25 * m
2. Divide both sides of the equation by 25: 50 / 25 = (25 * m) / 25
3. This simplifies to 2 = m

### Answer: m = 2 

Expected answer: 2

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 19 from both sides: 79 - 19 = ((6 * g) + 19) - 19 which simplifies to 60 = 6 * g
2. Divide both sides by 6: 60 / 6 = (6 * g) / 6 which simplifies to 10 = g
### Answer: g = 10 

Expected answer: 10

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Add 45 to both sides of the equation: 30 + 45 = (56 * l) - 45 + 45 which simplifies to 75 = 56 * l
2. Divide both sides of the equation by 56: 75 / 56 = (56 * l) / 56 which simplifies to l = 75/56

### Answer: l = 75/56 

Expected answer: 75/56

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 4 from both sides of the equation: 57 - 4 = ((11 * j) + 4) - 4, which simplifies to 53 = (11 * j)
2. Divide both sides of the equation by 11: 53 / 11 = (11 * j) / 11, which simplifies to j = 4.8181818182
### Answer: j = 4.8181818182 

Expected answer: 53/11

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
1. Add 56 to both sides of the equation: 
   36 + 56 = 34 * f - 56 + 56
   92 = 34 * f

2. Divide both sides of the equation by 34:
   92 / 34 = (34 * f) / 34
   2.71 = f (rounded to two decimal places)

### Answer: f = 2.71 

Expected answer: 46/17

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Add 43 to both sides of the equation to get all constant terms on one side: 56 + 43 = (70 * u) - 43 + 43, which simplifies to 99 = 70 * u. 
2. Divide both sides of the equation by 70 to isolate 'u': 99 / 70 = (70 * u) / 70.
3. This simplifies to u = 99/70 or u = 1.41 (rounded to two decimal places).

### Answer: u = 99/70 or u = 1.41 

Expected answer: 99/70

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 21 from both sides of the equation: 67 - 21 = 21 + 9*x - 21 which simplifies to 46 = 9*x
2. Divide both sides of the equation by 9: 46/9 = (9*x) / 9 which simplifies to 46/9 = x
### Answer: x = 46/9 

Expected answer: 46/9

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. Start by isolating the term with the unknown variable: 
   75 - 58 = 16 * i
   17 = 16 * i

2. Divide both sides of the equation by 16 to solve for 'i':
   17 / 16 = i

3. Calculate the result:
   1.0625 = i

### Answer: i = 1.0625 

Expected answer: 17/16

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
1. First, we simplify inside the parentheses: 111 = (54 + (39 * x))  ---> 111 = 54 + 39x
2. Next, subtract 54 from each side: 111-54 = 54 + 39x - 54   ---> 57 = 39x
3. Lastly, divide both sides by 39 to isolate x: 57 / 39 = 39x / 39  ---> 1.46 = x 

### Answer: x = 1.46 

Expected answer: 19/13

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 68 from both sides of the equation: 155 - 68 = (26 * o) + 68 - 68, which simplifies to 87 = 26 * o.
2. Divide both sides of the equation by 26: 87 / 26 = (26 * o) / 26.
3. This simplifies to o = 3.346.

### Answer: o = 3.346 

Expected answer: 87/26

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, add 17 to both sides of the equation: 7 + 17 = ((12 * p) - 17) + 17, which simplifies to 24 = 12 * p
Then, divide both sides of the equation by 12: 24 / 12 = (12 * p) / 12, which simplifies to 2 = p. 

### 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?

Gemini-1.5 Pro:

Reasoning: 
First, we simplify the equation by subtracting 93 from both sides: 163 - 93 = 93 + 55 * b - 93. This simplifies to 70 = 55 * b.
Then, to isolate 'b', we divide both sides of the equation by 55: 70 / 55 = (55 * b) / 55.
This gives us the value of 'b' as 1.27 when rounded to the nearest hundredth.

### Answer: b = 1.27 

Expected answer: 14/11

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Add 26 to both sides of the equation to isolate 'u': 62 + 26 = (u - 26) + 26
2. Simplify: 88 = u 

### Answer: u = 88. 

Expected answer: 88

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 93 from both sides: 179 - 93 = ((63 * a) + 93) - 93 which simplifies to 86 = 63 * a
2. Divide both sides by 63: 86 / 63 = (63 * a) / 63 which simplifies to a = 86/63

### Answer: a = 86/63 

Expected answer: 86/63

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, add 11 to both sides of the equation: 51 + 11 = (27 * c) - 11 + 11 which simplifies to 62 = 27 * c
Then, divide both sides of the equation by 27: 62 / 27 = (27 * c) / 27 which simplifies to 2.296 = c

### Answer: c = 2.296 

Expected answer: 62/27

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, add 18 to both sides of the equation: 19 + 18 = ((28 * d) - 18) + 18 which simplifies to 37 = 28 * d
Next, divide both sides of the equation by 28: 37 / 28 = (28 * d) / 28 which simplifies to  37/28 = d
### Answer: d = 37/28 

Expected answer: 37/28

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 62 from both sides of the equation: 159 - 62 = ((47 * e) + 62) - 62, which simplifies to 97 = 47 * e
2. Divide both sides of the equation by 47: 97 / 47 = (47 * e) / 47, which simplifies to 97 / 47 = e.
3. Calculate the result:  97 / 47 = 2.06

### Answer: e = 2.06 

Expected answer: 97/47

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1.  Subtract 50 from both sides: 145 - 50 = (50 + (91*g)) - 50, which simplifies to 95 = 91 * g
2. Divide both sides by 91:  95 / 91 = (91 * g) / 91, which simplifies to 1.044 = g

### Answer: g = 1.044 

Expected answer: 95/91

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
1. Subtract 73 from both sides of the equation: 123 - 73 = ((44 * l) + 73) - 73 which becomes 50 = 44 * l 
2. Divide both sides of the equation by 44:  50 / 44 = (44 * l) / 44
3. Simplify to get the value of l: l = 50 / 44 = 25 / 22

### Answer: l = 25/22 

Expected answer: 25/22

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
 1. Subtract 75 from both sides: 165-75 = ((19*q)+75)-75 which becomes 90 = 19*q
 2. Divide both sides by 19: 90/19 = (19*q)/19 which becomes 4.74 = q

### Answer: q= 4.74

Expected answer: 90/19

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
Step 1: Subtract 62 from both sides of the equation to isolate the term with 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
4.83333333 = g

### Answer: g = 4.83333333 

Expected answer: 29/6

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 21 from both sides of the equation to isolate the term with d: 84 - 21 = 20 * d + 21 - 21, which simplifies to 63 = 20 * d.
2. Divide both sides of the equation by 20 to solve for d: 63 / 20 = (20 * d) / 20.

### Answer: d = 3.15 

Expected answer: 63/20

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. **Simplify inside the parentheses:** 6 * g = 6g
2. **Subtract 50 from both sides:** 61 - 50 = 50 + 6g - 50 -->  11 = 6g
3. **Divide both sides by 6:** 11 / 6 = 6g / 6 --> 11/6 = g

### Answer: g = 11/6 

Expected answer: 11/6

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
1. Subtract 76 from both sides of the equation: 
126 - 76 = ((21 * v) + 76) - 76, which simplifies to 50 = 21 * v.

2. Divide both sides of the equation by 21:
50 / 21 = (21 * v) / 21, which simplifies to v = 50/21.

### Answer: v = 50/21 

Expected answer: 50/21

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, add 24 to both sides of the equation: 74 + 24 = ((91 * g) -24) + 24, which simplifies to  98 = 91 * g
Then, divide both sides of the equation by 91: 98 / 91 = (91 * g) / 91, which simplifies to 14/13 = g
### Answer: g = 14/13 

Expected answer: 14/13

Correct? Yes