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

Gemini-1.5 Flash:

Reasoning:
1. Subtract 92 from both sides of the equation: 122 - 92 = 92 + 28 * u - 92
2. Simplify: 30 = 28 * u
3. Divide both sides of the equation by 28: 30 / 28 = 28 * u / 28
4. Simplify: 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 Flash:

Here's how to solve the equation for 'i':

1. **Simplify the right side:** 
   42 = 35i - 34

2. **Add 34 to both sides:**
   42 + 34 = 35i

3. **Combine terms:**
   76 = 35i

4. **Divide both sides by 35:**
   76 / 35 = i

5. **Calculate the result:**
   i = 2.17 (approximately)

### Answer: i = 2.17 

Expected answer: 76/35

Correct? No

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

Gemini-1.5 Flash:

Reasoning: 
1. First, subtract 41 from both sides of the equation: 94 - 41 = 41 + 6 * r - 41
2. This simplifies to 53 = 6 * r
3. Now, divide both sides by 6: 53 / 6 = 6 * r / 6
4. This simplifies to 8.8333 = r

### Answer: 8.8333 

Expected answer: 53/6

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve for the value of 'i':

1. **Subtract 94 from both sides:** 
   158 - 94 = (19 * i) + 94 - 94
   This simplifies to: 64 = 19 * i

2. **Divide both sides by 19:**
   64 / 19 = (19 * i) / 19
   This simplifies to: i = 64/19

3. **Calculate the result:**
   i ≈ 3.37

### Answer: i ≈ 3.37 

Expected answer: 64/19

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the equation for 'q':

1. **Subtract 54 from both sides:** 
   134 - 54 = (30 * q) + 54 - 54
   80 = 30 * q

2. **Divide both sides by 30:**
   80 / 30 = (30 * q) / 30
   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 Flash:

Reasoning: To isolate 'y' on one side of the equation, we need to subtract 27 from both sides of the equation.
 
  94 - 27 = (27 + y) - 27
  
  This simplifies to:
  
  67 = y

### Answer: 67

Expected answer: 67

Correct? Yes

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

Gemini-1.5 Flash:

To solve for *h*, we need to isolate it on one side of the equation. Here's how:

1. **Add 70 to both sides:** 
   9 + 70 = (23 * h) - 70 + 70
   79 = 23 * h

2. **Divide both sides by 23:**
   79 / 23 = (23 * h) / 23
   3.43 = h

### Answer: 3.43 

Expected answer: 79/23

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Isolate the term with 't':**  Subtract 26 from both sides of the equation:
   92 - 26 = 33 * t + 26 - 26
   66 = 33 * t

2. **Solve for 't':** Divide both sides of the equation by 33:
   66 / 33 = (33 * t) / 33
   2 = t

### Answer: 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 Flash:

Here's how to solve the equation:

1. **Simplify the right side of the equation:**
   123 = 15e + 29

2. **Subtract 29 from both sides:**
   123 - 29 = 15e 
   94 = 15e

3. **Divide both sides by 15:**
   94 / 15 = e

4. **Simplify:**
   e = 6.27 (approximately)

### Answer: 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 Flash:

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

2. **Solve for 'k':**
   - Divide both sides of the equation by 75:
      96 / 75 = (75 * k) / 75
      1.28 = k

### Answer: 1.28 

Expected answer: 32/25

Correct? Yes

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

Gemini-1.5 Flash:

1. **Isolate the term with 'q'**:  Start by subtracting 89 from both sides of the equation:
   131 - 89 = (5 * q) + 89 - 89
   This simplifies to: 42 = 5 * q

2. **Solve for 'q'**: Now, divide both sides of the equation by 5:
   42 / 5 = (5 * q) / 5
   This gives us:  q = 8.4

### 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 Flash:

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

2. **Solve for 'p':**
   Divide both sides of the equation by 38:
   91 / 38 = (38 * p) / 38

3. **Calculate the result:**
   91 / 38 = p

4. **Simplify:**
   p = 2.3947 (approximately)

### Answer: 2.3947 

Expected answer: 91/38

Correct? No

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

Gemini-1.5 Flash:

1. **Isolate the term with 'j':**  Subtract 23 from both sides of the equation:
   76 - 23 = 42 * j + 23 - 23
   53 = 42 * j

2. **Solve for 'j':** Divide both sides of the equation by 42:
   53 / 42 = (42 * j) / 42
   1.26 = j

### Answer: 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 Flash:

Here's how to solve for 'l':

1. **Simplify the right side:** 
   - 25 * l = 25l
   - So, the equation becomes: 138 = 43 + 25l

2. **Isolate the term with 'l':**
   - Subtract 43 from both sides: 138 - 43 = 25l
   - This simplifies to: 95 = 25l

3. **Solve for 'l':**
   - Divide both sides by 25: 95 / 25 = l
   - This gives us: 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 Flash:

Reasoning:

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

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

### 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))

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Simplify the right side of the equation:** 
   77 = (33 + 14x)

2. **Subtract 33 from both sides:**
   77 - 33 = 14x

3. **Simplify:**
   44 = 14x

4. **Divide both sides by 14:**
   44 / 14 = x

5. **Simplify:**
   x = 22/7

### Answer: x = 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 Flash:

Here's how to solve the equation:

1. **Subtract 12 from both sides:** 
   110 - 12 = 12 + 88 * y - 12
   This simplifies to: 98 = 88 * y

2. **Divide both sides by 88:**
   98 / 88 = (88 * y) / 88
   This simplifies to: y = 98/88

3. **Simplify the fraction:**
   y = 49/44

### Answer: y = 49/44 

Expected answer: 49/44

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation:

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

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

### Answer: s = 99/82 

Expected answer: 99/82

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: 
1. Subtract 66 from both sides of the equation: 129 - 66 = 26 * m + 66 - 66
2. This simplifies to: 63 = 26 * m
3. Divide both sides by 26: 63/26 = 26 * m / 26
4. This results in: m = 63/26

### 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 Flash:

Here's how to solve for *q*:

1. **Simplify the right side of the equation:**
   82 = 27q - 17

2. **Isolate the term with *q* by adding 17 to both sides:**
   82 + 17 = 27q 
   99 = 27q

3. **Solve for *q* by dividing both sides by 27:**
   99 / 27 = q

4. **Simplify:**
   q = 3.67 (rounded to two decimal places)

### 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 Flash:

Here's how to solve the equation:

1. **Simplify the right side of the equation:**
   141 = (64 + 22k)

2. **Subtract 64 from both sides of the equation:**
   141 - 64 = 64 + 22k - 64
   77 = 22k

3. **Divide both sides of the equation by 22:**
   77 / 22 = 22k / 22
   3.5 = k

### Answer: 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 Flash:

1. **Isolate the term with 'v':** 
   Subtract 91 from both sides of the equation:
   175 - 91 = 91 + 45 * v - 91
   This simplifies to: 84 = 45 * v

2. **Solve for 'v':**
   Divide both sides of the equation by 45:
   84 / 45 = (45 * v) / 45

3. **Simplify:**
   This gives us: v = 1.87 (approximately)

### Answer: v = 1.87 (approximately) 

Expected answer: 28/15

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Isolate the term with 'k':** 
   - Add 18 to both sides of the equation:
     50 + 18 = (63 * k) - 18 + 18
     68 = 63 * k

2. **Solve for 'k':**
   - Divide both sides of the equation by 63:
     68 / 63 = (63 * k) / 63
     k = 68/63

3. **Simplify the answer (optional):** 
   - The fraction 68/63 can be left as is or simplified to a mixed number (1 5/63) or an approximate decimal (1.08).

### Answer: k = 68/63 

Expected answer: 68/63

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve for *l*:

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

2. **Divide both sides by 8:**
   75 / 8 = (8 * l) / 8
   9.375 = l

### Answer: 9.375 

Expected answer: 75/8

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Add 34 to both sides:** 
   5 + 34 = (10 * u) - 34 + 34
   39 = 10 * u

2. **Divide both sides by 10:**
   39 / 10 = (10 * u) / 10
   3.9 = u

### Answer: 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 Flash:

1. **Isolate the term with 'a'**: Subtract 61 from both sides of the equation: 
   91 - 61 = 9 * a + 61 - 61
   This simplifies to: 30 = 9 * a

2. **Solve for 'a'**: Divide both sides of the equation by 9:
   30 / 9 = (9 * a) / 9
   This simplifies to: 30/9 = a

3. **Simplify the fraction**:  The fraction 30/9 can be simplified by dividing both numerator and denominator by their greatest common factor, which is 3. 
   30/9 = (30/3) / (9/3) = 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 Flash:

Here's how to solve the equation for *i*:

1. **Isolate the term with *i*:** Subtract 61 from both sides of the equation:
   157 - 61 = 53 * i + 61 - 61
   This simplifies to: 96 = 53 * i

2. **Solve for *i*:** Divide both sides of the equation by 53:
   96 / 53 = (53 * i) / 53
   This simplifies to:  i = 96 / 53

3. **Simplify the result (if possible):** The fraction 96/53 cannot be simplified further.

### 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 Flash:

Here's how to solve the equation for the value of q:

1. **Simplify the right side of the equation:**
   71 = 24q + 14

2. **Subtract 14 from both sides of the equation:**
   71 - 14 = 24q + 14 - 14
   57 = 24q

3. **Divide both sides of the equation by 24:**
   57 / 24 = 24q / 24

4. **Simplify:**
   2.375 = q

### Answer: 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 Flash:

1. **Isolate the term with 'i':** 
   Subtract 96 from both sides of the equation:
   163 - 96 = 96 + 14 * i - 96
   This simplifies to: 67 = 14 * i

2. **Solve for 'i':**
   Divide both sides of the equation by 14:
   67 / 14 = (14 * i) / 14
   This simplifies to: i = 67 / 14

### Answer: i = 67/14 

Expected answer: 67/14

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve for 'e':

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

2. **Solve for 'e':**
   * Divide both sides by 70:
     82 / 70 = (70 * e) / 70
     e = 82/70

3. **Simplify the fraction (optional):**
     e = 41/35

### Answer: e = 41/35 

Expected answer: 41/35

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation for 'o':

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 gives us: o = 73/36

### Answer: o = 73/36 

Expected answer: 73/36

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation:

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

2. **Get rid of the negative sign:**
   Divide both sides of the equation by -1:
   22 = 13 * d

3. **Solve for 'd':**
   Divide both sides by 13:
   22 / 13 = d

4. **Simplify:**
   d ≈ 1.69

### Answer: d ≈ 1.69 

Expected answer: 22/13

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve for 'n':

1. **Isolate the term with 'n':** 
   Subtract 64 from both sides of the equation:
   118 - 64 = 64 + 6 * n - 64
   This simplifies to: 54 = 6 * n

2. **Solve for 'n':**
   Divide both sides of the equation by 6:
   54 / 6 = 6 * n / 6
   This simplifies to: 9 = n

### Answer: 9 

Expected answer: 9

Correct? Yes

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

Gemini-1.5 Flash:

1. **Simplify the right side of the equation:**
   (5 * d) - 7  = 5d - 7

2. **Rewrite the equation:**
   61 = 5d - 7

3. **Add 7 to both sides of the equation:**
   61 + 7 = 5d - 7 + 7
   68 = 5d

4. **Divide both sides of the equation by 5:**
   68 / 5 = 5d / 5
   13.6 = d

### Answer: 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 Flash:

1. **Simplify the right side of the equation:**
   79 = 8z - 18

2. **Isolate the term with 'z' by adding 18 to both sides:**
   79 + 18 = 8z - 18 + 18
   97 = 8z

3. **Solve for 'z' by dividing both sides by 8:**
   97 / 8 = 8z / 8
   12.125 = z

### Answer: 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 Flash:

Here's how to solve the equation:

1. **Simplify the right side:** 
   129 = 2z + 63

2. **Isolate the term with 'z':**
   Subtract 63 from both sides:
   129 - 63 = 2z
   66 = 2z

3. **Solve for 'z':**
   Divide both sides by 2:
   66 / 2 = z

4. **Simplify:**
   33 = z

### Answer: 33 

Expected answer: 33

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve for 'e':

1. **Simplify the right side:**
   127 = 29 + 32e

2. **Subtract 29 from both sides:**
   127 - 29 = 32e
   98 = 32e

3. **Divide both sides by 32:**
   98 / 32 = e

4. **Simplify:**
   e = 3.0625

### Answer: 3.0625 

Expected answer: 49/16

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning:
1. **Simplify the equation:**  Start by distributing the 50 inside the parentheses: 30 = 50x - 35
2. **Isolate the x term:** Add 35 to both sides of the equation: 30 + 35 = 50x - 35 + 35  which simplifies to 65 = 50x.
3. **Solve for x:** Divide both sides of the equation by 50: 65 / 50 = 50x / 50. This simplifies to x = 65/50.
4. **Simplify the fraction:** The fraction 65/50 can be simplified by dividing both numerator and denominator by 5, resulting in x = 13/10.

### Answer: x = 13/10 

Expected answer: 13/10

Correct? Yes

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

Gemini-1.5 Flash:

1. **Simplify the right side:** 
   * 10 * x = 10x
   * So the equation becomes: 66 = 9 + 10x

2. **Isolate the term with x:**
   * Subtract 9 from both sides: 66 - 9 = 9 + 10x - 9
   * This gives us: 57 = 10x

3. **Solve for x:**
   * Divide both sides by 10: 57 / 10 = 10x / 10
   * This results in: x = 5.7

### 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 Flash:

1. **Simplify the right side of the equation:**
   - 103 = (38a + 51)

2. **Subtract 51 from both sides:**
   - 103 - 51 = 38a + 51 - 51
   - 52 = 38a

3. **Divide both sides by 38:**
   - 52 / 38 = 38a / 38
   - 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 Flash:

Here's how to solve for 'f':

1. **Isolate the term with 'f':** 
   Subtract 8 from both sides of the equation:
   105 - 8 = 28 * f + 8 - 8
   This simplifies to: 97 = 28 * f

2. **Solve for 'f':**
   Divide both sides of the equation by 28:
   97 / 28 = (28 * f) / 28
   This simplifies to: f = 97/28

### Answer: f = 97/28 

Expected answer: 97/28

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation for *u*:

1. **Subtract 63 from both sides:**
   12 - 63 = 63 - 50*u - 63
   -51 = -50*u

2. **Divide both sides by -50:**
   -51 / -50 = -50*u / -50
   u = 51/50

### Answer: u = 51/50 

Expected answer: 51/50

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: 
1. Subtract 42 from both sides of the equation: 60 - 42 = 42 + (10 * b) - 42
2. This simplifies to 18 = 10 * b
3. Divide both sides by 10: 18 / 10 = (10 * b) / 10
4. This simplifies to b = 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)

Gemini-1.5 Flash:

Here's how to solve the equation for 'j':

1. **Subtract 13 from both sides:** 
   84 - 13 = (25 * j) + 13 - 13
   71 = 25 * j

2. **Divide both sides by 25:**
   71 / 25 = (25 * j) / 25
   2.84 = j

### 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 Flash:

Here's how to solve the equation:

1. **Isolate the term with 's':** 
   Subtract 91 from both sides of the equation:
   153 - 91 = 91 + 5s - 91
   This simplifies to: 62 = 5s

2. **Solve for 's':**
   Divide both sides of the equation by 5:
   62 / 5 = 5s / 5
   This simplifies to: s = 12.4

### 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 Flash:

1. **Simplify inside the parentheses:**  30 * g = 30g
   The equation now looks like this: 65 = (22 + 30g)

2. **Remove the parentheses:**  Since there's only addition inside the parentheses, we can simply remove them.
   The equation is now: 65 = 22 + 30g

3. **Isolate the term with 'g':** Subtract 22 from both sides of the equation.
   65 - 22 = 22 + 30g - 22
   This simplifies to: 43 = 30g

4. **Solve for 'g':** Divide both sides of the equation by 30.
   43 / 30 = 30g / 30
   This simplifies to: g = 43/30

### 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 Flash:

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:**
   86 / 29 = (29 * f) / 29
   This simplifies to: f = 86/29

3. **Simplify the fraction:**
   f ≈ 2.97

### Answer: f ≈ 2.97 

Expected answer: 86/29

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve for 'q':

1. **Simplify the right side of the equation:** 
   *  14 * q = 14q
   *  19 + 14q 

2. **Rewrite the equation:**
   *  80 = 19 + 14q

3. **Isolate the term with 'q':**
   * Subtract 19 from both sides: 80 - 19 = 14q
   * Simplify: 61 = 14q

4. **Solve for 'q':**
   * Divide both sides by 14: 61 / 14 = q

5. **Simplify:**
   * q ≈ 4.36

### Answer: q ≈ 4.36 

Expected answer: 61/14

Correct? No

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

Gemini-1.5 Flash:

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

2. Divide both sides of the equation by 46:
   50 / 46 = (46 * m) / 46

3. Simplify:
   m = 50/46

4. Reduce the fraction to its simplest form:
    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 Flash:

1. **Isolate the term with 'i':** 
   Subtract 13 from both sides of the equation:
   68 - 13 = 13 + 6 * i - 13
   This simplifies to: 55 = 6 * i

2. **Solve for 'i':**
   Divide both sides of the equation by 6:
   55 / 6 = (6 * i) / 6
   This simplifies to:  i = 55/6

### Answer: i = 55/6 

Expected answer: 55/6

Correct? Yes

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

Gemini-1.5 Flash:

1. **Isolate the term with 'h':** 
   - Add 61 to both sides of the equation:
     25 + 61 = (74 * h) - 61 + 61
     86 = 74 * h

2. **Solve for 'h':**
   - Divide both sides of the equation by 74:
     86 / 74 = (74 * h) / 74
     h = 86 / 74

3. **Simplify the fraction:**
     h = 43 / 37

### Answer: h = 43/37 

Expected answer: 43/37

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Simplify the right side of the equation:**
   (6 * q) - 30 = 6q - 30

2. **Add 30 to both sides of the equation:**
   51 + 30 = 6q - 30 + 30
   81 = 6q

3. **Divide both sides of the equation by 6:**
   81 / 6 = 6q / 6
   13.5 = q

### Answer: 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 Flash:

Reasoning: 
1. Subtract 81 from both sides of the equation: 38 - 81 = 81 - 36 * r - 81
2. Simplify: -43 = -36 * r
3. Divide both sides of the equation by -36: -43 / -36 = -36 * r / -36
4. Simplify: 43/36 = r

### Answer: 43/36 

Expected answer: 43/36

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Simplify inside the parentheses:** 
   * 56 * a = 56a

2. **Rewrite the equation:**
   * 90 = 23 + 56a

3. **Isolate the term with 'a':**
   * Subtract 23 from both sides: 
      * 90 - 23 = 56a
      * 67 = 56a

4. **Solve for 'a':**
   * Divide both sides by 56:
      * 67 / 56 = a

5. **Simplify:**
   * a = 1.1964 (approximately)

### Answer: a = 1.1964 (approximately) 

Expected answer: 67/56

Correct? No

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

Gemini-1.5 Flash:

Reasoning:
1. Subtract 13 from both sides of the equation: 81 - 13 = 13 + 30 * h - 13 
2. This simplifies to 68 = 30 * h
3. Divide both sides of the equation by 30: 68/30 = 30 * h / 30
4. This simplifies to 68/30 = h

### Answer: h = 68/30 

Expected answer: 34/15

Correct? Yes

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

Gemini-1.5 Flash:

1. **Simplify the right side of the equation:** 
   160 = 62m + 69

2. **Subtract 69 from both sides:**
   160 - 69 = 62m + 69 - 69
   91 = 62m

3. **Divide both sides by 62:**
   91 / 62 = 62m / 62
   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 Flash:

Reasoning: 
1. Subtract 69 from both sides of the equation: 
  100 - 69 = 69 + 28 * q - 69
  31 = 28 * q
2. Divide both sides of the equation by 28:
  31 / 28 = 28 * q / 28
  31/28 = q

### 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)

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Subtract 94 from both sides:** 
   192 - 94 = (98 * w) + 94 - 94
   98 = 98 * w

2. **Divide both sides by 98:**
   98 / 98 = (98 * w) / 98
   1 = w

### Answer: 1 

Expected answer: 1

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning:
1. Start by simplifying the right side of the equation by performing the multiplication: 
   40 = 93 - (33 * y)
   40 = 93 - 33y

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

3. Divide both sides of the equation by -33 to solve for 'y':
   -53 / -33 = -33y / -33
   y = 53/33

### Answer: y = 53/33 

Expected answer: 53/33

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve for the unknown variable 'u':

1. **Isolate the term with 'u':** 
   - Add 20 to both sides of the equation: 
     74 + 20 = (48 * u) - 20 + 20
     94 = 48 * u

2. **Solve for 'u':**
   - Divide both sides of the equation by 48:
     94 / 48 = (48 * u) / 48
     u = 94 / 48

3. **Simplify the fraction (optional):**
    - The fraction 94/48 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:
       u = (94/2) / (48/2) = 47/24 

### Answer: u = 47/24 

Expected answer: 47/24

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation for the variable *f*:

1. **Add 76 to both sides:** 
   13 + 76 = (86 * f) - 76 + 76
   89 = 86 * f

2. **Divide both sides by 86:**
   89 / 86 = (86 * f) / 86
   1.035 = f

### Answer: f = 1.035 

Expected answer: 89/86

Correct? No

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

Gemini-1.5 Flash:

Reasoning:
1. Begin by subtracting 36 from both sides of the equation:
   122 - 36 = (36 + (56 * c)) - 36
   This simplifies to 86 = 56 * c

2. Next, divide both sides of the equation by 56 to isolate c:
   86 / 56 = (56 * c) / 56

3. This gives us c = 86/56

4. Finally, simplify the fraction:
   c = 43/28

### Answer: c = 43/28 

Expected answer: 43/28

Correct? Yes

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

Gemini-1.5 Flash:

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

2. Divide both sides by 81 to isolate q:
87 / 81 = (81 * q) / 81
This simplifies to:
q = 87/81

3. Simplify the fraction: 
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 Flash:

Here's how to solve for 'u':

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

2. **Solve for 'u':**
   Divide both sides of the equation by 42:
   43 / 42 = (42 * u) / 42
   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 Flash:

Reasoning:
1. Start by simplifying the right side of the equation: 103 = (52 + (6 * j))
   - 103 = 52 + 6j
2. Subtract 52 from both sides of the equation: 
   - 103 - 52 = 52 + 6j - 52
   - 51 = 6j
3. Divide both sides of the equation by 6:
   - 51 / 6 = 6j / 6
   - 8.5 = j

### Answer: 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 Flash:

Here's how to solve the equation:

1. **Simplify inside the parentheses:** 
   56 = (82 - 4n)

2. **Subtract 82 from both sides:**
   56 - 82 = (82 - 4n) - 82
   -26 = -4n

3. **Divide both sides by -4:**
   -26 / -4 = -4n / -4
   6.5 = n

### Answer: 6.5 

Expected answer: 13/2

Correct? Yes

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

Gemini-1.5 Flash:

1. **Isolate the term with 'm':** 
   Subtract 14 from both sides of the equation:
   77 - 14 = 14 + 60 * m - 14
   This simplifies to: 63 = 60 * m

2. **Solve for 'm':**
   Divide both sides of the equation by 60:
   63 / 60 = 60 * m / 60

3. **Simplify:**
   This gives us: m = 1.05

### 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 Flash:

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

1. **Subtract 17 from both sides:**
   31 - 17 = 17 + e - 17

2. **Simplify:**
   14 = e

### 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 Flash:

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

2. **Solve for 'x':**
   - Divide both sides by -15:
      -79 / -15 = -(15 * x) / -15
      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 Flash:

Reasoning: First, we need to isolate the term containing 'e'. To do that, subtract 88 from both sides of the equation: 
177 - 88 = 88 + 6 * e - 88 

This simplifies to: 
89 = 6 * e

Now, to get 'e' by itself, we divide both sides of the equation by 6:
89 / 6 = 6 * e / 6

This gives us:
e = 89 / 6

### Answer: e = 89/6 

Expected answer: 89/6

Correct? Yes

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

Gemini-1.5 Flash:

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, which simplifies to 26.67 = r.

### Answer: 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 Flash:

Here's how to solve the equation for the value of 'v':

1. **Simplify the right side:** 
   154 = (70 + 31v)

2. **Subtract 70 from both sides:**
   154 - 70 = 31v

3. **Simplify:**
   84 = 31v

4. **Divide both sides by 31:**
   84 / 31 = v

5. **Calculate:**
   v ≈ 2.71

### 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 Flash:

Here's how to solve the equation for the value of r:

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

2. **Solve for 'r':**
   - Divide both sides of the equation by 70:
      92 / 70 = (70 * r) / 70
      1.3143 ≈ r

### Answer: 1.3143 

Expected answer: 46/35

Correct? No

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

Gemini-1.5 Flash:

1. **Simplify the right side:** 
   * Multiply 19 and r: 19 * r = 19r
   * The equation becomes: 93 = (19r + 2)

2. **Isolate the term with 'r':**
   * Subtract 2 from both sides of the equation:
      93 - 2 = 19r + 2 - 2
      91 = 19r

3. **Solve for 'r':**
   * Divide both sides by 19:
      91 / 19 = 19r / 19
      r = 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))

Gemini-1.5 Flash:

Here's how to solve the equation step-by-step:

1. **Simplify the right side:** 
   20 = 67 - 37z

2. **Subtract 67 from both sides:**
   20 - 67 = -37z

3. **Combine like terms:**
   -47 = -37z

4. **Divide both sides by -37:**
   -47 / -37 = z

5. **Simplify:**
   z = 1.27 (approximately)

### Answer: 1.27 

Expected answer: 47/37

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the equation for 'm':

1. **Simplify the equation:**
   -  65 = 25m + 15

2. **Isolate the term with 'm':**
   - Subtract 15 from both sides: 65 - 15 = 25m 
   - This simplifies to 50 = 25m

3. **Solve for 'm':**
   - Divide both sides by 25: 50 / 25 = m

4. **Simplify:**
   - 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 Flash:

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

2. **Divide both sides of the equation by 6:**
   60 / 6 = (6 * g) / 6
   10 = g

### Answer: 10 

Expected answer: 10

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation for 'l':

1. **Simplify the right side:** 
   30 = 56l - 45

2. **Add 45 to both sides:**
   30 + 45 = 56l

3. **Combine like terms:**
   75 = 56l

4. **Divide both sides by 56:**
   75 / 56 = l

5. **Simplify the fraction (optional):**
   l = 1.339 (rounded to three decimal places)

### Answer: l = 1.339 

Expected answer: 75/56

Correct? No

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

Gemini-1.5 Flash:

Reasoning:
1. Subtract 4 from both sides of the equation: 57 - 4 = (11 * j) + 4 - 4
2. Simplify: 53 = 11 * j
3. Divide both sides by 11: 53/11 = (11 * j) / 11
4. Simplify: 53/11 = j

### Answer: j = 53/11 

Expected answer: 53/11

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation for 'f':

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

2. **Solve for 'f':**
   - Divide both sides of the equation by 34:
     92 / 34 = (34 * f) / 34
     2.71 = f

### 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

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Isolate the term with 'u':**
   Add 43 to both sides of the equation: 
   56 + 43 = (70 * u) - 43 + 43
   This simplifies to: 99 = 70 * u

2. **Solve for 'u':**
   Divide both sides of the equation by 70:
   99 / 70 = (70 * u) / 70
   This simplifies to: u = 99/70

### Answer: u = 99/70 

Expected answer: 99/70

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: 
1. Subtract 21 from both sides of the equation: 
67 - 21 = 21 + 9*x - 21
This simplifies to: 
46 = 9*x

2. Divide both sides of the equation by 9:
46/9 = 9*x/9
This simplifies to:
x = 46/9

### 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 Flash:

1. **Simplify the right side of the equation:**
   * 16 * i = 16i
   * (58 + 16i) remains as is.

2. **Now the equation is:** 75 = (58 + 16i)

3. **Isolate the term with the unknown variable (16i):**
   * Subtract 58 from both sides of the equation: 
      75 - 58 = 58 + 16i - 58
      17 = 16i

4. **Solve for 'i':**
   * Divide both sides of the equation by 16:
      17 / 16 = 16i / 16
      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 Flash:

Reasoning:
1. Subtract 54 from both sides of the equation: 111 - 54 = (39 * x) 
2. This simplifies to: 57 = (39 * x)
3. Divide both sides by 39 to isolate x: 57/39 = x
4. Simplify the fraction: 1.46 = x

### Answer: 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 Flash:

Here's how to solve the equation for 'o':

1. **Simplify the right side:**
   *  (26 * o) + 68 = 26o + 68

2. **Isolate the term with 'o':**
   * Subtract 68 from both sides of the equation:
      155 - 68 = 26o + 68 - 68
      87 = 26o

3. **Solve for 'o':**
   * Divide both sides by 26:
      87 / 26 = 26o / 26
      3.35 = o 

### Answer: 3.35 

Expected answer: 87/26

Correct? No

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

Gemini-1.5 Flash:

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

2. **Solve for 'p':** Divide both sides of the equation by 12:
   24 / 12 = (12 * p) / 12
   2 = p

### Answer: p = 2 

Expected answer: 2

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning:
1.  First, we need to isolate the term with 'b' by subtracting 93 from both sides of the equation: 163 - 93 = 55 * b.
2. This simplifies to 70 = 55 * b.
3. Now, divide both sides by 55 to find the value of 'b': 70/55 = b.
4.  Finally, simplify the fraction: 70/55 = 14/11 = b.

### Answer: b = 14/11 

Expected answer: 14/11

Correct? Yes

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

Gemini-1.5 Flash:

To solve for 'u', we need to isolate it on one side of the equation. We can do this by following these steps:

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

2. **Simplify:**
   88 = u

Therefore, the value of 'u' is 88.

### Answer: 88 

Expected answer: 88

Correct? Yes

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

Gemini-1.5 Flash:

1. **Isolate the term with 'a':**  Start by subtracting 93 from both sides of the equation:
   179 - 93 = (63 * a) + 93 - 93
   86 = 63 * a

2. **Solve for 'a':** Divide both sides of the equation by 63:
   86 / 63 = (63 * a) / 63
   a = 86 / 63

3. **Simplify (optional):**  The fraction 86/63 can be left as is, or you can express it as a mixed number or decimal:
   a = 1 23/63  (mixed number)
   a ≈ 1.38 (decimal)

### 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 Flash:

Reasoning: 
1. Add 11 to both sides of the equation: 51 + 11 = (27 * c) - 11 + 11
2. Simplify: 62 = 27 * c
3. Divide both sides of the equation by 27: 62 / 27 = (27 * c) / 27
4. Simplify: 62/27 = c

### Answer: 62/27 

Expected answer: 62/27

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the equation for 'd':

1. **Simplify the right side:** 
   19 = 28d - 18

2. **Add 18 to both sides:**
   19 + 18 = 28d 
   37 = 28d

3. **Divide both sides by 28:**
   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 Flash:

Here's how to solve the equation:

1. **Subtract 62 from both sides:** 
   159 - 62 = (47 * e) + 62 - 62
   97 = 47 * e

2. **Divide both sides by 47:**
   97 / 47 = (47 * e) / 47
   e = 97 / 47

3. **Simplify the fraction (if possible):**
   e ≈ 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 Flash:

Here's how to solve the equation:

1. **Simplify the right side of the equation:**
   145 = 50 + 91g

2. **Subtract 50 from both sides:**
   145 - 50 = 50 + 91g - 50
   95 = 91g

3. **Divide both sides by 91:**
   95 / 91 = 91g / 91
   g = 95 / 91

4. **Simplify the fraction (optional):**
   g ≈ 1.04

### Answer: g ≈ 1.04 

Expected answer: 95/91

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the equation for the value of *l*:

1. **Subtract 73 from both sides:**
   123 - 73 = (44 * l) + 73 - 73
   50 = 44 * l

2. **Divide both sides by 44:**
   50 / 44 = (44 * l) / 44
   1.136 = l

### Answer: 1.136 

Expected answer: 25/22

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the equation:

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

2. **Divide both sides by 19:**
   90 / 19 = (19 * q) / 19
   4.74 = q

### Answer: 4.74 

Expected answer: 90/19

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the equation:

1. **Simplify the right side of the equation:**
   149 = 18g + 62

2. **Subtract 62 from both sides:**
   149 - 62 = 18g + 62 - 62
   87 = 18g

3. **Divide both sides by 18:**
   87 / 18 = 18g / 18
   4.8333... = g

**Therefore, the value of g is approximately 4.8333.** 

### Answer: 4.8333 

Expected answer: 29/6

Correct? No

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

Gemini-1.5 Flash:

1. **Isolate the term with 'd':**  Subtract 21 from both sides of the equation:
   84 - 21 = 20 * d + 21 - 21
   This simplifies to: 63 = 20 * d

2. **Solve for 'd':** Divide both sides of the equation by 20:
   63 / 20 = (20 * d) / 20
   This simplifies to: d = 63/20

3. **Simplify the fraction:** The fraction can be left as 63/20 or expressed as a decimal (3.15). 

### Answer: d = 63/20 or 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 Flash:

1. **Simplify inside the parentheses:** 
   (50 + (6 * g)) becomes (50 + 6g)

2. **Rewrite the equation:**
   61 = 50 + 6g

3. **Isolate the term with 'g':**
   Subtract 50 from both sides of the equation:
   61 - 50 = 50 + 6g - 50
   11 = 6g

4. **Solve for 'g':**
   Divide both sides of the equation by 6:
   11 / 6 = 6g / 6
   g = 11/6

### 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 Flash:

Here's how to solve the equation:

1. **Simplify the right side:**  
   126 = 21v + 76

2. **Subtract 76 from both sides:**
   126 - 76 = 21v + 76 - 76
   50 = 21v

3. **Divide both sides by 21:**
   50 / 21 = 21v / 21
   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 Flash:

Here's how to solve for 'g':

1. **Add 24 to both sides of the equation:** 
   74 + 24 = (91 * g) - 24 + 24
   This simplifies to: 98 = 91 * g

2. **Divide both sides by 91:**
   98 / 91 = (91 * g) / 91

3. **Simplify:**
   g = 98/91

### Answer: g = 98/91 

Expected answer: 14/13

Correct? Yes