GPT-4o on 8.EE.C.7
Common Core Standard 8.EE.C.7
This standard covers the following:
Solve linear equations in one variable.
Problem: Solve the following equation for the variable u: 122 = 92 + 28 * u
GPT-4o:
To solve the equation \( 122 = 92 + 28u \) for the variable \( u \), follow these steps:
1. Subtract 92 from both sides of the equation to isolate the term with \( u \):
\[
122 - 92 = 28u
\]
2. Simplify the left side:
\[
30 = 28u
\]
3. Divide both sides by 28 to solve for \( u \):
\[
u = \frac{30}{28}
\]
4. Simplify the fraction:
\[
u = \frac{15}{14}
\]
### Answer: \( \frac{15}{14} \)
Expected answer: 15/14
Correct? Yes
Problem: Solve the following equation for i: 42 = ((35 * i) - 34)
GPT-4o:
To solve the equation \( 42 = 35i - 34 \) for \( i \), follow these steps:
1. Start with the given equation:
\[
42 = 35i - 34
\]
2. Add 34 to both sides of the equation to isolate the term with \( i \):
\[
42 + 34 = 35i
\]
3. Simplify the left side:
\[
76 = 35i
\]
4. Divide both sides by 35 to solve for \( i \):
\[
i = \frac{76}{35}
\]
5. Simplify the fraction if possible:
\[
i = \frac{76}{35}
\]
### Answer: \( \frac{76}{35} \)
Expected answer: 76/35
Correct? Yes
Problem: Solve the following equation to find the value of r: 94 = 41 + 6 * r
GPT-4o:
To solve the equation \( 94 = 41 + 6r \) for \( r \), follow these steps:
1. Subtract 41 from both sides of the equation to isolate the term with \( r \):
\[
94 - 41 = 6r
\]
2. Simplify the left side:
\[
53 = 6r
\]
3. Divide both sides by 6 to solve for \( r \):
\[
r = \frac{53}{6}
\]
4. Simplify the fraction if possible:
\[
r = 8.8333\ldots \quad \text{(or as a fraction, } \frac{53}{6} \text{)}
\]
### Answer: \( r = \frac{53}{6} \) or \( r \approx 8.8333 \)
Expected answer: 53/6
Correct? Yes
Problem: Determine the value of "i" from the following equation: 158 = ((19 * i) + 94)
GPT-4o:
To determine the value of \( i \) from the equation \( 158 = 19i + 94 \), we need to isolate \( i \). Here are the steps:
1. Start with the given equation:
\[
158 = 19i + 94
\]
2. Subtract 94 from both sides to isolate the term with \( i \):
\[
158 - 94 = 19i
\]
3. Simplify the left side:
\[
64 = 19i
\]
4. Divide both sides by 19 to solve for \( i \):
\[
i = \frac{64}{19}
\]
5. Simplify the fraction if possible. In this case, \( \frac{64}{19} \) is already in its simplest form.
### Answer: \(\frac{64}{19}\)
Expected answer: 64/19
Correct? Yes
Problem: Solve the following equation for 'q': 134 = ((30 * q) + 54)
GPT-4o:
To solve the equation \( 134 = 30q + 54 \) for \( q \), follow these steps:
1. Subtract 54 from both sides of the equation to isolate the term with \( q \):
\[
134 - 54 = 30q
\]
2. Simplify the left side:
\[
80 = 30q
\]
3. Divide both sides by 30 to solve for \( q \):
\[
q = \frac{80}{30}
\]
4. Simplify the fraction:
\[
q = \frac{8}{3}
\]
### Answer: \( \frac{8}{3} \)
Expected answer: 8/3
Correct? Yes
Problem: Solve the following linear equation to find the value of y: 94 = (27 + y)
GPT-4o:
To solve the linear equation \( 94 = 27 + y \), we need to isolate \( y \). Step 1: Subtract 27 from both sides of the equation to isolate \( y \): \[ 94 - 27 = y \] Step 2: Perform the subtraction: \[ 67 = y \] Thus, the value of \( y \) is 67. ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: Solve the following linear equation for the value of h: 9 = ((23 * h) - 70)
GPT-4o:
To solve the linear equation \( 9 = 23h - 70 \) for \( h \), follow these steps:
1. Start with the given equation:
\[
9 = 23h - 70
\]
2. Add 70 to both sides of the equation to isolate the term with \( h \):
\[
9 + 70 = 23h - 70 + 70
\]
Simplifying the left side:
\[
79 = 23h
\]
3. Divide both sides by 23 to solve for \( h \):
\[
\frac{79}{23} = \frac{23h}{23}
\]
Simplifying the right side:
\[
h = \frac{79}{23}
\]
4. Perform the division:
\[
h = \frac{79}{23} \approx 3.4348
\]
### Answer: \( h \approx 3.4348 \)
Expected answer: 79/23
Correct? No
Problem: Solve the following equation to find the value of t: 92 = 33 * t + 26
GPT-4o:
To solve the equation \( 92 = 33t + 26 \) for \( t \), follow these steps:
1. Subtract 26 from both sides of the equation to isolate the term with \( t \):
\[
92 - 26 = 33t
\]
Simplifying the left side:
\[
66 = 33t
\]
2. Divide both sides by 33 to solve for \( t \):
\[
t = \frac{66}{33}
\]
Simplifying the fraction:
\[
t = 2
\]
### Answer: 2
Expected answer: 2
Correct? Yes
Problem: Solve the following linear equation to find the value of e: 123 = ((15 * e) + 29).
GPT-4o:
To solve the linear equation \( 123 = 15e + 29 \), we need to isolate the variable \( e \). Here are the steps:
1. Subtract 29 from both sides of the equation to get rid of the constant term on the right side:
\[
123 - 29 = 15e
\]
2. Simplify the left side:
\[
94 = 15e
\]
3. Divide both sides by 15 to solve for \( e \):
\[
e = \frac{94}{15}
\]
4. Simplify the fraction if possible:
\[
e = \frac{94}{15} \approx 6.27
\]
### Answer: \( e = \frac{94}{15} \) or approximately 6.27.
Expected answer: 94/15
Correct? Yes
Problem: Solve the following equation to find the value of 'k': 16 = ((75 * k) - 80)
GPT-4o:
To solve the equation \( 16 = 75k - 80 \) for \( k \), follow these steps:
1. Add 80 to both sides of the equation to isolate the term with \( k \):
\[
16 + 80 = 75k - 80 + 80
\]
Simplifying this, we get:
\[
96 = 75k
\]
2. Divide both sides of the equation by 75 to solve for \( k \):
\[
k = \frac{96}{75}
\]
3. Simplify the fraction:
\[
k = \frac{96 \div 3}{75 \div 3} = \frac{32}{25}
\]
### Answer: \( \frac{32}{25} \)
Expected answer: 32/25
Correct? Yes
Problem: Solve for q in the following equation: 131 = ((5 * q) + 89)
GPT-4o:
To solve for \( q \) in the equation \( 131 = 5q + 89 \), follow these steps:
1. Subtract 89 from both sides of the equation to isolate the term with \( q \):
\[
131 - 89 = 5q
\]
2. Simplify the left side:
\[
42 = 5q
\]
3. Divide both sides by 5 to solve for \( q \):
\[
q = \frac{42}{5}
\]
4. Simplify the fraction:
\[
q = 8.4
\]
### Answer: 8.4
Expected answer: 42/5
Correct? Yes
Problem: Find the value of p that satisfies the following equation: 147 = ((38 * p) + 56)
GPT-4o:
To find the value of \( p \) that satisfies the equation \( 147 = (38p + 56) \), we need to isolate \( p \). Here are the steps:
1. Start with the given equation:
\[
147 = 38p + 56
\]
2. Subtract 56 from both sides to isolate the term with \( p \):
\[
147 - 56 = 38p
\]
3. Simplify the left side:
\[
91 = 38p
\]
4. Divide both sides by 38 to solve for \( p \):
\[
p = \frac{91}{38}
\]
5. Simplify the fraction if possible:
\[
p = \frac{91}{38} = 2.394736842105263
\]
### Answer: 2.394736842105263
Expected answer: 91/38
Correct? No
Problem: Solve the following equation to find the value of 'j': 76 = 42 * j + 23
GPT-4o:
To solve the equation \( 76 = 42j + 23 \) for \( j \), follow these steps:
1. Subtract 23 from both sides of the equation to isolate the term with \( j \):
\[
76 - 23 = 42j
\]
Simplifying the left side:
\[
53 = 42j
\]
2. Divide both sides by 42 to solve for \( j \):
\[
j = \frac{53}{42}
\]
3. Simplify the fraction if possible. In this case, 53 and 42 have no common factors other than 1, so the fraction is already in its simplest form:
\[
j = \frac{53}{42}
\]
### Answer: \(\frac{53}{42}\)
Expected answer: 53/42
Correct? Yes
Problem: Solve the following equation to find the value of 'l': 138 = 43 + 25 * l
GPT-4o:
To solve the equation \( 138 = 43 + 25l \) for \( l \), follow these steps:
1. Subtract 43 from both sides of the equation to isolate the term with \( l \):
\[
138 - 43 = 25l
\]
2. Simplify the left side:
\[
95 = 25l
\]
3. Divide both sides by 25 to solve for \( l \):
\[
l = \frac{95}{25}
\]
4. Simplify the fraction:
\[
l = 3.8
\]
### Answer: 3.8
Expected answer: 19/5
Correct? Yes
Problem: Solve the following equation to find the unknown w: 80 = ((24 * w) + 35)
GPT-4o:
To solve the equation \( 80 = 24w + 35 \) for \( w \), follow these steps:
1. Subtract 35 from both sides of the equation to isolate the term with \( w \):
\[
80 - 35 = 24w
\]
Simplifying the left side:
\[
45 = 24w
\]
2. Divide both sides by 24 to solve for \( w \):
\[
w = \frac{45}{24}
\]
3. Simplify the fraction:
\[
w = \frac{15}{8}
\]
### Answer: \(\frac{15}{8}\)
Expected answer: 15/8
Correct? Yes
Problem: Solve the following linear equation to find the value of x: 77 = (33 + (14 * x))
GPT-4o:
To solve the linear equation \( 77 = 33 + 14x \), we need to isolate \( x \). Here are the steps:
1. Subtract 33 from both sides of the equation to get rid of the constant term on the right side:
\[
77 - 33 = 33 + 14x - 33
\]
Simplifying this, we get:
\[
44 = 14x
\]
2. Next, divide both sides of the equation by 14 to solve for \( x \):
\[
\frac{44}{14} = \frac{14x}{14}
\]
Simplifying this, we get:
\[
x = \frac{44}{14}
\]
3. Simplify the fraction:
\[
x = \frac{22}{7}
\]
### Answer: \(\frac{22}{7}\)
Expected answer: 22/7
Correct? Yes
Problem: Solve the following linear equation to find the value of y: 110 = 12 + 88 * y
GPT-4o:
To solve the linear equation \( 110 = 12 + 88y \), we need to isolate the variable \( y \). Here are the steps:
1. Subtract 12 from both sides of the equation to get rid of the constant term on the right side:
\[
110 - 12 = 88y
\]
Simplifying the left side:
\[
98 = 88y
\]
2. Divide both sides of the equation by 88 to solve for \( y \):
\[
y = \frac{98}{88}
\]
3. Simplify the fraction:
\[
y = \frac{49}{44}
\]
So, the value of \( y \) is \( \frac{49}{44} \).
### Answer: \(\frac{49}{44}\)
Expected answer: 49/44
Correct? Yes
Problem: Solve the following linear equation for the variable 's': 179 = 82 * s + 80
GPT-4o:
To solve the linear equation \( 179 = 82s + 80 \) for the variable \( s \), follow these steps:
1. Subtract 80 from both sides of the equation to isolate the term with \( s \):
\[
179 - 80 = 82s + 80 - 80
\]
Simplifying this, we get:
\[
99 = 82s
\]
2. Divide both sides of the equation by 82 to solve for \( s \):
\[
s = \frac{99}{82}
\]
3. Simplify the fraction if possible. In this case, 99 and 82 have no common factors other than 1, so the fraction is already in its simplest form:
\[
s = \frac{99}{82}
\]
### Answer: \(\frac{99}{82}\)
Expected answer: 99/82
Correct? Yes
Problem: Solve the following equation for m: 129 = 26 * m + 66
GPT-4o:
To solve the equation \( 129 = 26m + 66 \) for \( m \), follow these steps:
1. Subtract 66 from both sides of the equation to isolate the term with \( m \):
\[
129 - 66 = 26m
\]
Simplifying the left side:
\[
63 = 26m
\]
2. Divide both sides of the equation by 26 to solve for \( m \):
\[
m = \frac{63}{26}
\]
3. Simplify the fraction if possible. In this case, 63 and 26 have no common factors other than 1, so the fraction is already in its simplest form:
\[
m = \frac{63}{26}
\]
### Answer: \( \frac{63}{26} \)
Expected answer: 63/26
Correct? Yes
Problem: Solve the following linear equation for q: 82 = ((27 * q) - 17)
GPT-4o:
To solve the linear equation for \( q \):
\[ 82 = 27q - 17 \]
First, isolate the term with \( q \) by adding 17 to both sides of the equation:
\[ 82 + 17 = 27q - 17 + 17 \]
This simplifies to:
\[ 99 = 27q \]
Next, solve for \( q \) by dividing both sides by 27:
\[ q = \frac{99}{27} \]
Simplify the fraction:
\[ q = \frac{99 \div 9}{27 \div 9} = \frac{11}{3} \]
### Answer: \(\frac{11}{3}\)
Expected answer: 11/3
Correct? Yes
Problem: Solve the following linear equation for the variable k: 141 = (64 + (22 * k))
GPT-4o:
To solve the linear equation for the variable \( k \):
\[ 141 = 64 + 22k \]
First, isolate the term containing \( k \) by subtracting 64 from both sides of the equation:
\[ 141 - 64 = 22k \]
Simplify the left side:
\[ 77 = 22k \]
Next, solve for \( k \) by dividing both sides by 22:
\[ k = \frac{77}{22} \]
Simplify the fraction:
\[ k = 3.5 \]
### Answer: 3.5
Expected answer: 7/2
Correct? Yes
Problem: Determine the value of 'v' by solving this linear equation: 175 = 91 + 45 * v
GPT-4o:
To solve for \( v \) in the equation \( 175 = 91 + 45v \), follow these steps:
1. Subtract 91 from both sides of the equation to isolate the term with \( v \):
\[
175 - 91 = 45v
\]
2. Simplify the left side:
\[
84 = 45v
\]
3. Divide both sides by 45 to solve for \( v \):
\[
v = \frac{84}{45}
\]
4. Simplify the fraction by finding the greatest common divisor (GCD) of 84 and 45, which is 3:
\[
v = \frac{84 \div 3}{45 \div 3} = \frac{28}{15}
\]
### Answer: \(\frac{28}{15}\)
Expected answer: 28/15
Correct? Yes
Problem: Solve the following equation for the value of k: 50 = ((63 * k) - 18)
GPT-4o:
To solve the equation \( 50 = 63k - 18 \) for \( k \), follow these steps:
1. Start by isolating the term with \( k \) on one side of the equation. Add 18 to both sides of the equation:
\[
50 + 18 = 63k - 18 + 18
\]
Simplifying this, we get:
\[
68 = 63k
\]
2. Next, solve for \( k \) by dividing both sides of the equation by 63:
\[
k = \frac{68}{63}
\]
Thus, the value of \( k \) is:
### Answer: \(\frac{68}{63}\)
Expected answer: 68/63
Correct? Yes
Problem: Solve the following equation for l: 65 = ((8 * l) - 10)
GPT-4o:
To solve the equation \( 65 = 8l - 10 \) for \( l \), follow these steps:
1. Start with the given equation:
\[
65 = 8l - 10
\]
2. Add 10 to both sides of the equation to isolate the term with \( l \):
\[
65 + 10 = 8l - 10 + 10
\]
Simplifying this, we get:
\[
75 = 8l
\]
3. Divide both sides of the equation by 8 to solve for \( l \):
\[
\frac{75}{8} = \frac{8l}{8}
\]
Simplifying this, we get:
\[
l = \frac{75}{8}
\]
4. Simplify the fraction if possible:
\[
l = 9.375
\]
### Answer: 9.375
Expected answer: 75/8
Correct? Yes
Problem: Solve the following equation: 5 = ((10 * u) - 34)
GPT-4o:
To solve the equation \( 5 = 10u - 34 \), we need to isolate the variable \( u \). Here are the steps:
1. Start with the given equation:
\[
5 = 10u - 34
\]
2. Add 34 to both sides of the equation to move the constant term on the right side to the left side:
\[
5 + 34 = 10u - 34 + 34
\]
Simplifying this, we get:
\[
39 = 10u
\]
3. Divide both sides of the equation by 10 to solve for \( u \):
\[
\frac{39}{10} = \frac{10u}{10}
\]
Simplifying this, we get:
\[
3.9 = u
\]
### Answer: 3.9
Expected answer: 39/10
Correct? Yes
Problem: Solve the following problem in linear equations for variable 'a': 91 = 9 * a + 61
GPT-4o:
To solve the equation \( 91 = 9a + 61 \) for the variable \( a \), follow these steps:
1. Subtract 61 from both sides of the equation to isolate the term with \( a \):
\[
91 - 61 = 9a + 61 - 61
\]
Simplifying this, we get:
\[
30 = 9a
\]
2. Divide both sides of the equation by 9 to solve for \( a \):
\[
\frac{30}{9} = \frac{9a}{9}
\]
Simplifying this, we get:
\[
a = \frac{30}{9} = \frac{10}{3}
\]
### Answer: \( \frac{10}{3} \)
Expected answer: 10/3
Correct? Yes
Problem: Solve the following linear equation for the variable i: 157 = 53 * i + 61
GPT-4o:
To solve the linear equation for the variable \( i \), we need to isolate \( i \) on one side of the equation. Here are the steps:
1. Start with the given equation:
\[
157 = 53i + 61
\]
2. Subtract 61 from both sides to isolate the term with \( i \):
\[
157 - 61 = 53i
\]
3. Simplify the left side:
\[
96 = 53i
\]
4. Divide both sides by 53 to solve for \( i \):
\[
i = \frac{96}{53}
\]
5. Simplify the fraction if possible. In this case, 96 and 53 have no common factors other than 1, so the fraction is already in its simplest form.
### Answer: \( \frac{96}{53} \)
Expected answer: 96/53
Correct? Yes
Problem: Solve the following linear equation for the value of q: 71 = ((24 * q) + 14)
GPT-4o:
To solve the linear equation \( 71 = 24q + 14 \) for \( q \), follow these steps:
1. Subtract 14 from both sides of the equation to isolate the term with \( q \):
\[
71 - 14 = 24q
\]
Simplifying the left side:
\[
57 = 24q
\]
2. Divide both sides by 24 to solve for \( q \):
\[
q = \frac{57}{24}
\]
3. Simplify the fraction if possible:
\[
q = \frac{57}{24} = \frac{19}{8}
\]
### Answer: \(\frac{19}{8}\)
Expected answer: 19/8
Correct? Yes
Problem: Solve the following linear equation for the value of i: 163 = 96 + 14 * i
GPT-4o:
To solve the linear equation \( 163 = 96 + 14i \) for \( i \), follow these steps:
1. Subtract 96 from both sides of the equation to isolate the term with \( i \):
\[
163 - 96 = 14i
\]
2. Simplify the left side:
\[
67 = 14i
\]
3. Divide both sides by 14 to solve for \( i \):
\[
i = \frac{67}{14}
\]
4. Simplify the fraction if possible:
\[
i = \frac{67}{14}
\]
Since 67 and 14 have no common factors other than 1, the fraction is already in its simplest form.
### Answer: \( \frac{67}{14} \)
Expected answer: 67/14
Correct? Yes
Problem: Solve the following linear equation for the value of e: 59 = (70 * e) - 23
GPT-4o:
To solve the linear equation \( 59 = 70e - 23 \) for \( e \), follow these steps:
1. Start by isolating the term with \( e \) on one side of the equation. Add 23 to both sides of the equation:
\[
59 + 23 = 70e - 23 + 23
\]
Simplifying this, we get:
\[
82 = 70e
\]
2. Next, solve for \( e \) by dividing both sides of the equation by 70:
\[
e = \frac{82}{70}
\]
3. Simplify the fraction:
\[
e = \frac{41}{35}
\]
Thus, the value of \( e \) is:
### Answer: \(\frac{41}{35}\)
Expected answer: 41/35
Correct? Yes
Problem: Solve the following linear equation for o: 147 = 36 * o + 74
GPT-4o:
To solve the linear equation for \( o \), we need to isolate \( o \) on one side of the equation. Here are the steps:
1. Start with the given equation:
\[
147 = 36o + 74
\]
2. Subtract 74 from both sides to isolate the term with \( o \):
\[
147 - 74 = 36o
\]
3. Simplify the left side:
\[
73 = 36o
\]
4. Divide both sides by 36 to solve for \( o \):
\[
o = \frac{73}{36}
\]
Thus, the value of \( o \) is:
### Answer: \(\frac{73}{36}\)
Expected answer: 73/36
Correct? Yes
Problem: Solve the following equation: 71 = 93 - (13 * d)
GPT-4o:
To solve the equation \( 71 = 93 - (13 \cdot d) \), we need to isolate the variable \( d \). Here are the steps:
1. Start with the given equation:
\[
71 = 93 - 13d
\]
2. Subtract 93 from both sides to isolate the term involving \( d \):
\[
71 - 93 = -13d
\]
3. Simplify the left side:
\[
-22 = -13d
\]
4. Divide both sides by -13 to solve for \( d \):
\[
d = \frac{-22}{-13}
\]
5. Simplify the fraction:
\[
d = \frac{22}{13}
\]
### Answer: \(\frac{22}{13}\)
Expected answer: 22/13
Correct? Yes
Problem: Solve the following equation to find the value of n: 118 = 64 + 6 * n
GPT-4o:
To solve the equation \( 118 = 64 + 6n \), we need to isolate the variable \( n \). Here are the steps:
1. Subtract 64 from both sides of the equation to get:
\[
118 - 64 = 6n
\]
2. Simplify the left side:
\[
54 = 6n
\]
3. Divide both sides by 6 to solve for \( n \):
\[
n = \frac{54}{6}
\]
4. Simplify the division:
\[
n = 9
\]
### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Solve the following equation to find the value of 'd': 61 = ((5 * d) - 7)
GPT-4o:
To solve the equation \( 61 = (5d - 7) \), we need to isolate the variable \( d \). Here are the steps:
1. Start with the given equation:
\[
61 = 5d - 7
\]
2. Add 7 to both sides of the equation to eliminate the constant term on the right side:
\[
61 + 7 = 5d - 7 + 7
\]
Simplifying this, we get:
\[
68 = 5d
\]
3. Divide both sides of the equation by 5 to solve for \( d \):
\[
\frac{68}{5} = \frac{5d}{5}
\]
Simplifying this, we get:
\[
d = \frac{68}{5}
\]
4. Simplify the fraction:
\[
d = 13.6
\]
### Answer: 13.6
Expected answer: 68/5
Correct? Yes
Problem: Solve the following linear equation for the value of z: 79 = ((8 * z) - 18)
GPT-4o:
To solve the linear equation \( 79 = 8z - 18 \) for \( z \), follow these steps:
1. Start with the given equation:
\[
79 = 8z - 18
\]
2. Add 18 to both sides of the equation to isolate the term with \( z \):
\[
79 + 18 = 8z - 18 + 18
\]
Simplifying the left side:
\[
97 = 8z
\]
3. Divide both sides by 8 to solve for \( z \):
\[
\frac{97}{8} = z
\]
4. Simplify the fraction if possible:
\[
z = 12.125
\]
### Answer: 12.125
Expected answer: 97/8
Correct? Yes
Problem: Solve the following linear equation for the value of z: 129 = ((2 * z) + 63)
GPT-4o:
To solve the linear equation for \( z \), we start with the given equation:
\[ 129 = 2z + 63 \]
First, we need to isolate the term containing \( z \). We do this by subtracting 63 from both sides of the equation:
\[ 129 - 63 = 2z \]
Simplifying the left side:
\[ 66 = 2z \]
Next, we solve for \( z \) by dividing both sides by 2:
\[ \frac{66}{2} = z \]
Simplifying the right side:
\[ z = 33 \]
### Answer: 33
Expected answer: 33
Correct? Yes
Problem: Solve the following linear equation for e: 127 = (29 + (32 * e))
GPT-4o:
To solve the linear equation \(127 = 29 + 32e\), we need to isolate the variable \(e\). Here are the steps:
1. Subtract 29 from both sides of the equation to isolate the term with \(e\):
\[
127 - 29 = 32e
\]
2. Simplify the left side:
\[
98 = 32e
\]
3. Divide both sides by 32 to solve for \(e\):
\[
e = \frac{98}{32}
\]
4. Simplify the fraction:
\[
e = \frac{49}{16}
\]
### Answer: \(\frac{49}{16}\)
Expected answer: 49/16
Correct? Yes
Problem: Solve the following linear equation for the value of x: 30 = ((50 * x) - 35)
GPT-4o:
To solve the linear equation \( 30 = 50x - 35 \), follow these steps:
1. Add 35 to both sides of the equation to isolate the term with \( x \):
\[
30 + 35 = 50x - 35 + 35
\]
Simplifying this, we get:
\[
65 = 50x
\]
2. Divide both sides by 50 to solve for \( x \):
\[
x = \frac{65}{50}
\]
3. Simplify the fraction:
\[
x = \frac{65 \div 5}{50 \div 5} = \frac{13}{10} = 1.3
\]
### Answer: 1.3
Expected answer: 13/10
Correct? Yes
Problem: Solve the following equation for x: 66 = 9 + 10 * x
GPT-4o:
To solve the equation \( 66 = 9 + 10x \) for \( x \), follow these steps:
1. Subtract 9 from both sides of the equation to isolate the term with \( x \):
\[
66 - 9 = 10x
\]
Simplifying the left side:
\[
57 = 10x
\]
2. Divide both sides by 10 to solve for \( x \):
\[
x = \frac{57}{10}
\]
Simplifying the fraction:
\[
x = 5.7
\]
### Answer: 5.7
Expected answer: 57/10
Correct? Yes
Problem: Solve the following algebraic equation for the unknown variable a: 103 = ((38 * a) + 51)
GPT-4o:
To solve the equation \( 103 = 38a + 51 \) for the unknown variable \( a \), follow these steps:
1. Subtract 51 from both sides of the equation to isolate the term with \( a \):
\[
103 - 51 = 38a
\]
2. Simplify the left side:
\[
52 = 38a
\]
3. Divide both sides by 38 to solve for \( a \):
\[
a = \frac{52}{38}
\]
4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:
\[
a = \frac{52 \div 2}{38 \div 2} = \frac{26}{19}
\]
### Answer: \( \frac{26}{19} \)
Expected answer: 26/19
Correct? Yes
Problem: Determine the value of f in the following equation: 105 = 28 * f + 8
GPT-4o:
To determine the value of \( f \) in the equation \( 105 = 28f + 8 \), we need to isolate \( f \). Here are the steps:
1. Subtract 8 from both sides of the equation:
\[
105 - 8 = 28f
\]
Simplifying the left side:
\[
97 = 28f
\]
2. Divide both sides by 28 to solve for \( f \):
\[
f = \frac{97}{28}
\]
3. Simplify the fraction if possible. In this case, 97 and 28 have no common factors other than 1, so the fraction is already in its simplest form.
### Answer: \( \frac{97}{28} \)
Expected answer: 97/28
Correct? Yes
Problem: Solve the linear equation for u: 12 = 63 - 50 * u
GPT-4o:
To solve the linear equation for \( u \):
\[ 12 = 63 - 50u \]
First, isolate the term with \( u \) on one side of the equation. Subtract 63 from both sides:
\[ 12 - 63 = -50u \]
Simplify the left side:
\[ -51 = -50u \]
Next, divide both sides by -50 to solve for \( u \):
\[ u = \frac{-51}{-50} \]
Simplify the fraction:
\[ u = \frac{51}{50} \]
### Answer: \( \frac{51}{50} \)
Expected answer: 51/50
Correct? Yes
Problem: Solve the following equation for the value of 'b': 60 = 42 + (10 * b)
GPT-4o:
To solve the equation \( 60 = 42 + (10 \cdot b) \) for the value of \( b \), follow these steps:
1. Subtract 42 from both sides of the equation to isolate the term with \( b \):
\[
60 - 42 = 10 \cdot b
\]
2. Simplify the left side:
\[
18 = 10 \cdot b
\]
3. Divide both sides by 10 to solve for \( b \):
\[
b = \frac{18}{10}
\]
4. Simplify the fraction:
\[
b = 1.8
\]
### Answer: 1.8
Expected answer: 9/5
Correct? Yes
Problem: Solve the following linear equation for the variable 'j': 84 = ((25 * j) + 13)
GPT-4o:
To solve the linear equation for the variable \( j \), we start with the given equation:
\[ 84 = 25j + 13 \]
First, we need to isolate the term containing \( j \). We do this by subtracting 13 from both sides of the equation:
\[ 84 - 13 = 25j \]
Simplifying the left side:
\[ 71 = 25j \]
Next, we solve for \( j \) by dividing both sides of the equation by 25:
\[ j = \frac{71}{25} \]
Simplifying the fraction:
\[ j = 2.84 \]
### Answer: 2.84
Expected answer: 71/25
Correct? Yes
Problem: Solve the following linear equation for s: 153 = 91 + 5 * s
GPT-4o:
To solve the linear equation \( 153 = 91 + 5s \) for \( s \), follow these steps:
1. Subtract 91 from both sides of the equation to isolate the term with \( s \):
\[
153 - 91 = 5s
\]
2. Simplify the left side:
\[
62 = 5s
\]
3. Divide both sides by 5 to solve for \( s \):
\[
s = \frac{62}{5}
\]
4. Simplify the fraction:
\[
s = 12.4
\]
### Answer: 12.4
Expected answer: 62/5
Correct? Yes
Problem: Solve for g in the following equation: 65 = (22 + (30 * g))
GPT-4o:
To solve for \( g \) in the equation \( 65 = 22 + 30g \), follow these steps:
1. Subtract 22 from both sides of the equation to isolate the term with \( g \):
\[
65 - 22 = 30g
\]
Simplifying the left side:
\[
43 = 30g
\]
2. Divide both sides by 30 to solve for \( g \):
\[
g = \frac{43}{30}
\]
3. Simplify the fraction if possible. In this case, \( \frac{43}{30} \) is already in its simplest form.
### Answer: \( \frac{43}{30} \)
Expected answer: 43/30
Correct? Yes
Problem: Solve the following linear equation for the value of f: 96 = ((29 * f) + 10)
GPT-4o:
To solve the linear equation for \( f \), we start with the given equation:
\[ 96 = 29f + 10 \]
First, we need to isolate the term containing \( f \). We do this by subtracting 10 from both sides of the equation:
\[ 96 - 10 = 29f \]
This simplifies to:
\[ 86 = 29f \]
Next, we solve for \( f \) by dividing both sides of the equation by 29:
\[ f = \frac{86}{29} \]
Simplifying the fraction:
\[ f = 2.96551724137931 \]
Since the problem does not specify the need for rounding, we can leave the answer in its exact form.
### Answer: 2.96551724137931
Expected answer: 86/29
Correct? No
Problem: Solve the following equation for the variable q: 80 = (19 + (14 * q))
GPT-4o:
To solve the equation \( 80 = 19 + 14q \) for the variable \( q \), follow these steps:
1. Subtract 19 from both sides of the equation to isolate the term with \( q \):
\[
80 - 19 = 14q
\]
2. Simplify the left side:
\[
61 = 14q
\]
3. Divide both sides by 14 to solve for \( q \):
\[
q = \frac{61}{14}
\]
4. Simplify the fraction if possible. In this case, 61 and 14 have no common factors other than 1, so the fraction is already in its simplest form:
\[
q = \frac{61}{14}
\]
### Answer: \( \frac{61}{14} \)
Expected answer: 61/14
Correct? Yes
Problem: Solve the following linear equation for the variable 'm': 145 = 95 + 46 * m
GPT-4o:
To solve the linear equation for the variable \( m \):
\[ 145 = 95 + 46m \]
First, isolate the term containing \( m \) by subtracting 95 from both sides of the equation:
\[ 145 - 95 = 46m \]
Simplify the left side:
\[ 50 = 46m \]
Next, solve for \( m \) by dividing both sides by 46:
\[ m = \frac{50}{46} \]
Simplify the fraction:
\[ m = \frac{25}{23} \]
### Answer: \(\frac{25}{23}\)
Expected answer: 25/23
Correct? Yes
Problem: Solve the following equation for the value of 'i': 68 = 13 + 6 * i
GPT-4o:
To solve the equation \( 68 = 13 + 6i \) for \( i \), follow these steps:
1. Subtract 13 from both sides of the equation to isolate the term with \( i \):
\[
68 - 13 = 6i
\]
Simplifying the left side:
\[
55 = 6i
\]
2. Divide both sides by 6 to solve for \( i \):
\[
i = \frac{55}{6}
\]
3. Simplify the fraction if possible. In this case, \( \frac{55}{6} \) is already in its simplest form.
### Answer: \( \frac{55}{6} \)
Expected answer: 55/6
Correct? Yes
Problem: Solve the following equation for the value of h: 25 = ((74 * h) - 61)
GPT-4o:
To solve the equation \( 25 = 74h - 61 \) for \( h \), follow these steps:
1. Start by isolating the term with \( h \) on one side of the equation. Add 61 to both sides of the equation:
\[
25 + 61 = 74h - 61 + 61
\]
Simplifying this, we get:
\[
86 = 74h
\]
2. Next, solve for \( h \) by dividing both sides of the equation by 74:
\[
h = \frac{86}{74}
\]
3. Simplify the fraction if possible:
\[
h = \frac{43}{37}
\]
### Answer: \(\frac{43}{37}\)
Expected answer: 43/37
Correct? Yes
Problem: Solve the following linear equation for the value of q: 51 = ((6 * q) - 30)
GPT-4o:
To solve the linear equation \( 51 = 6q - 30 \), we need to isolate the variable \( q \). Here are the steps:
1. Start with the given equation:
\[
51 = 6q - 30
\]
2. Add 30 to both sides of the equation to move the constant term on the right side to the left side:
\[
51 + 30 = 6q - 30 + 30
\]
Simplifying this, we get:
\[
81 = 6q
\]
3. Divide both sides of the equation by 6 to solve for \( q \):
\[
\frac{81}{6} = \frac{6q}{6}
\]
Simplifying this, we get:
\[
q = 13.5
\]
### Answer: 13.5
Expected answer: 27/2
Correct? Yes
Problem: Find the value of r in the following linear equation: 38 = 81 - 36 * r
GPT-4o:
To find the value of \( r \) in the equation \( 38 = 81 - 36r \), we need to isolate \( r \). Here are the steps:
1. Start with the given equation:
\[
38 = 81 - 36r
\]
2. Subtract 81 from both sides to move the constant term to the left side:
\[
38 - 81 = -36r
\]
3. Simplify the left side:
\[
-43 = -36r
\]
4. Divide both sides by -36 to solve for \( r \):
\[
r = \frac{-43}{-36}
\]
5. Simplify the fraction:
\[
r = \frac{43}{36}
\]
### Answer: \(\frac{43}{36}\)
Expected answer: 43/36
Correct? Yes
Problem: Solve the following equation: 90 = (23 + (56 * a))
GPT-4o:
To solve the equation \( 90 = 23 + 56a \), we need to isolate the variable \( a \).
1. Start by subtracting 23 from both sides of the equation:
\[
90 - 23 = 56a
\]
Simplifying the left side:
\[
67 = 56a
\]
2. Next, divide both sides by 56 to solve for \( a \):
\[
a = \frac{67}{56}
\]
3. Simplify the fraction if possible:
\[
a = \frac{67}{56}
\]
Since 67 and 56 have no common factors other than 1, the fraction is already in its simplest form.
### Answer: \( \frac{67}{56} \)
Expected answer: 67/56
Correct? Yes
Problem: Solve the following linear equation for the unknown variable h: 81 = 13 + 30 * h
GPT-4o:
To solve the linear equation \( 81 = 13 + 30h \) for the unknown variable \( h \), follow these steps:
1. Subtract 13 from both sides of the equation to isolate the term with \( h \):
\[
81 - 13 = 30h
\]
2. Simplify the left side:
\[
68 = 30h
\]
3. Divide both sides by 30 to solve for \( h \):
\[
h = \frac{68}{30}
\]
4. Simplify the fraction:
\[
h = \frac{34}{15}
\]
### Answer: \( \frac{34}{15} \)
Expected answer: 34/15
Correct? Yes
Problem: Solve the following linear equation for the value of m: 160 = ((62 * m) + 69)
GPT-4o:
To solve the linear equation \( 160 = 62m + 69 \) for \( m \), follow these steps:
1. Subtract 69 from both sides of the equation to isolate the term with \( m \):
\[
160 - 69 = 62m
\]
Simplifying the left side:
\[
91 = 62m
\]
2. Divide both sides by 62 to solve for \( m \):
\[
m = \frac{91}{62}
\]
3. Simplify the fraction if possible. In this case, 91 and 62 have no common factors other than 1, so the fraction is already in its simplest form:
\[
m = \frac{91}{62}
\]
### Answer: \(\frac{91}{62}\)
Expected answer: 91/62
Correct? Yes
Problem: Solve the following equation to find the value of q: 100 = 69 + 28 * q
GPT-4o:
To solve the equation \( 100 = 69 + 28q \) for \( q \), follow these steps:
1. Subtract 69 from both sides of the equation to isolate the term with \( q \):
\[
100 - 69 = 28q
\]
2. Simplify the left side:
\[
31 = 28q
\]
3. Divide both sides by 28 to solve for \( q \):
\[
q = \frac{31}{28}
\]
4. Simplify the fraction if possible. In this case, \( \frac{31}{28} \) is already in its simplest form.
### Answer: \(\frac{31}{28}\)
Expected answer: 31/28
Correct? Yes
Problem: Solve the following linear equation to find the value of w: 192 = ((98 * w) + 94)
GPT-4o:
To solve the linear equation \( 192 = 98w + 94 \), we need to isolate the variable \( w \). Here are the steps:
1. Subtract 94 from both sides of the equation to get rid of the constant term on the right side:
\[
192 - 94 = 98w
\]
2. Simplify the left side:
\[
98 = 98w
\]
3. Divide both sides by 98 to solve for \( w \):
\[
w = \frac{98}{98}
\]
4. Simplify the fraction:
\[
w = 1
\]
### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Solve the following equation to find the value of y: 40 = 93 - 33 * y
GPT-4o:
To solve the equation \( 40 = 93 - 33y \) for \( y \), follow these steps:
1. Subtract 93 from both sides of the equation to isolate the term involving \( y \):
\[
40 - 93 = -33y
\]
2. Simplify the left side:
\[
-53 = -33y
\]
3. Divide both sides by -33 to solve for \( y \):
\[
y = \frac{-53}{-33}
\]
4. Simplify the fraction:
\[
y = \frac{53}{33}
\]
### Answer: \(\frac{53}{33}\)
Expected answer: 53/33
Correct? Yes
Problem: Solve for the unknown variable u in the following linear equation: 74 = ((48 * u) - 20)
GPT-4o:
To solve for the unknown variable \( u \) in the equation \( 74 = 48u - 20 \), follow these steps:
1. Start with the given equation:
\[
74 = 48u - 20
\]
2. Add 20 to both sides of the equation to isolate the term with \( u \):
\[
74 + 20 = 48u
\]
3. Simplify the left side:
\[
94 = 48u
\]
4. Divide both sides by 48 to solve for \( u \):
\[
u = \frac{94}{48}
\]
5. Simplify the fraction by finding the greatest common divisor (GCD) of 94 and 48, which is 2:
\[
u = \frac{94 \div 2}{48 \div 2} = \frac{47}{24}
\]
### Answer: \(\frac{47}{24}\)
Expected answer: 47/24
Correct? Yes
Problem: Solve the following equation for the variable f: 13 = ((86 * f) - 76)
GPT-4o:
To solve the equation \( 13 = 86f - 76 \) for the variable \( f \), follow these steps:
1. Add 76 to both sides of the equation to isolate the term with \( f \):
\[
13 + 76 = 86f - 76 + 76
\]
Simplifying this, we get:
\[
89 = 86f
\]
2. Divide both sides of the equation by 86 to solve for \( f \):
\[
f = \frac{89}{86}
\]
3. Simplify the fraction if possible. In this case, \( \frac{89}{86} \) is already in its simplest form.
### Answer: \( \frac{89}{86} \)
Expected answer: 89/86
Correct? Yes
Problem: Solve the following equation for c: 122 = (36 + (56 * c))
GPT-4o:
To solve the equation \( 122 = 36 + 56c \) for \( c \), follow these steps:
1. Subtract 36 from both sides of the equation to isolate the term with \( c \):
\[
122 - 36 = 56c
\]
2. Simplify the left side:
\[
86 = 56c
\]
3. Divide both sides by 56 to solve for \( c \):
\[
c = \frac{86}{56}
\]
4. Simplify the fraction:
\[
c = \frac{43}{28}
\]
### Answer: \( \frac{43}{28} \)
Expected answer: 43/28
Correct? Yes
Problem: Solve the following linear equation for the unknown quantity q: 186 = 99 + 81 * q
GPT-4o:
To solve the linear equation for the unknown quantity \( q \), we start with the given equation:
\[ 186 = 99 + 81q \]
First, we need to isolate the term containing \( q \). We do this by subtracting 99 from both sides of the equation:
\[ 186 - 99 = 81q \]
Simplifying the left side:
\[ 87 = 81q \]
Next, we solve for \( q \) by dividing both sides of the equation by 81:
\[ q = \frac{87}{81} \]
Simplifying the fraction:
\[ q = \frac{87 \div 3}{81 \div 3} = \frac{29}{27} \]
Thus, the value of \( q \) is:
### Answer: \(\frac{29}{27}\)
Expected answer: 29/27
Correct? Yes
Problem: Find the value of 'u' in the following equation: 120 = ((42 * u) + 77)
GPT-4o:
To find the value of \( u \) in the equation \( 120 = (42u + 77) \), we need to isolate \( u \). Here are the steps:
1. Start with the given equation:
\[
120 = 42u + 77
\]
2. Subtract 77 from both sides to isolate the term with \( u \):
\[
120 - 77 = 42u
\]
3. Simplify the left side:
\[
43 = 42u
\]
4. Divide both sides by 42 to solve for \( u \):
\[
u = \frac{43}{42}
\]
### Answer: \(\frac{43}{42}\)
Expected answer: 43/42
Correct? Yes
Problem: Solve the following equation to find the value of j: 103 = (52 + (6 * j))
GPT-4o:
To solve the equation \( 103 = 52 + (6 \cdot j) \), we need to isolate the variable \( j \). Here are the steps:
1. Start with the given equation:
\[
103 = 52 + (6 \cdot j)
\]
2. Subtract 52 from both sides to isolate the term with \( j \):
\[
103 - 52 = 6 \cdot j
\]
3. Simplify the left side:
\[
51 = 6 \cdot j
\]
4. Divide both sides by 6 to solve for \( j \):
\[
j = \frac{51}{6}
\]
5. Simplify the fraction:
\[
j = 8.5
\]
### Answer: 8.5
Expected answer: 17/2
Correct? Yes
Problem: Solve the following linear equation for the value of n: 56 = (82 - (4 * n))
GPT-4o:
To solve the linear equation \( 56 = 82 - 4n \), we need to isolate the variable \( n \). Here are the steps:
1. Start with the given equation:
\[
56 = 82 - 4n
\]
2. Subtract 82 from both sides to isolate the term involving \( n \):
\[
56 - 82 = -4n
\]
3. Simplify the left side:
\[
-26 = -4n
\]
4. Divide both sides by -4 to solve for \( n \):
\[
n = \frac{-26}{-4}
\]
5. Simplify the fraction:
\[
n = \frac{26}{4} = 6.5
\]
### Answer: 6.5
Expected answer: 13/2
Correct? Yes
Problem: Solve the following linear equation for m: 77 = 14 + 60 * m
GPT-4o:
To solve the linear equation \( 77 = 14 + 60m \) for \( m \), follow these steps:
1. Subtract 14 from both sides of the equation to isolate the term with \( m \):
\[
77 - 14 = 60m
\]
2. Simplify the left side:
\[
63 = 60m
\]
3. Divide both sides by 60 to solve for \( m \):
\[
m = \frac{63}{60}
\]
4. Simplify the fraction:
\[
m = \frac{21}{20}
\]
### Answer: \( \frac{21}{20} \)
Expected answer: 21/20
Correct? Yes
Problem: Solve the following linear equation for the variable 'e': 31 = 17 + e
GPT-4o:
To solve the linear equation for the variable \( e \), we need to isolate \( e \) on one side of the equation. Here are the steps: 1. Start with the given equation: \[ 31 = 17 + e \] 2. Subtract 17 from both sides of the equation to isolate \( e \): \[ 31 - 17 = e \] 3. Simplify the left side: \[ 14 = e \] Thus, the value of \( e \) is 14. ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: Find the value of x that solves the following equation: 2 = 81 - (15 * x)
GPT-4o:
To find the value of \( x \) that solves the equation \( 2 = 81 - 15x \), we need to isolate \( x \). Here are the steps:
1. Start with the given equation:
\[
2 = 81 - 15x
\]
2. Subtract 81 from both sides to move the constant term to the left side:
\[
2 - 81 = -15x
\]
3. Simplify the left side:
\[
-79 = -15x
\]
4. Divide both sides by -15 to solve for \( x \):
\[
x = \frac{-79}{-15}
\]
5. Simplify the fraction:
\[
x = \frac{79}{15}
\]
### Answer: \(\frac{79}{15}\)
Expected answer: 79/15
Correct? Yes
Problem: Solve the following equation for the value of e: 177 = 88 + 6 * e.
GPT-4o:
To solve the equation \( 177 = 88 + 6e \) for \( e \), follow these steps:
1. Subtract 88 from both sides of the equation to isolate the term with \( e \):
\[
177 - 88 = 6e
\]
2. Simplify the left side:
\[
89 = 6e
\]
3. Divide both sides by 6 to solve for \( e \):
\[
e = \frac{89}{6}
\]
4. Simplify the fraction if possible:
\[
e = 14.8333\ldots \quad \text{(or as a fraction, } \frac{89}{6} \text{)}
\]
### Answer: \( \frac{89}{6} \) or approximately 14.8333
Expected answer: 89/6
Correct? Yes
Problem: Solve the following equation to find the value of 'r': 95 = 3*r + 15
GPT-4o:
To solve the equation \( 95 = 3r + 15 \), we need to isolate the variable \( r \). Here are the steps:
1. Subtract 15 from both sides of the equation to get rid of the constant term on the right side:
\[
95 - 15 = 3r + 15 - 15
\]
Simplifying this, we get:
\[
80 = 3r
\]
2. Next, divide both sides of the equation by 3 to solve for \( r \):
\[
\frac{80}{3} = \frac{3r}{3}
\]
Simplifying this, we get:
\[
r = \frac{80}{3}
\]
### Answer: \(\frac{80}{3}\)
Expected answer: 80/3
Correct? Yes
Problem: Solve the following linear equation for the value of v: 154 = (70 + (31 * v))
GPT-4o:
To solve the linear equation \( 154 = 70 + 31v \) for \( v \), follow these steps:
1. Subtract 70 from both sides of the equation to isolate the term with \( v \):
\[
154 - 70 = 31v
\]
Simplifying the left side:
\[
84 = 31v
\]
2. Divide both sides by 31 to solve for \( v \):
\[
v = \frac{84}{31}
\]
3. Simplify the fraction if possible:
\[
v = \frac{84}{31}
\]
Since 84 and 31 have no common factors other than 1, the fraction is already in its simplest form.
### Answer: \( v = \frac{84}{31} \)
Expected answer: 84/31
Correct? Yes
Problem: Solve the following equation for the value of r: 179 = ((70 * r) + 87)
GPT-4o:
To solve the equation \( 179 = 70r + 87 \) for \( r \), follow these steps:
1. Subtract 87 from both sides of the equation to isolate the term with \( r \):
\[
179 - 87 = 70r
\]
2. Simplify the left side:
\[
92 = 70r
\]
3. Divide both sides by 70 to solve for \( r \):
\[
r = \frac{92}{70}
\]
4. Simplify the fraction:
\[
r = \frac{46}{35}
\]
Thus, the value of \( r \) is:
### Answer: \(\frac{46}{35}\)
Expected answer: 46/35
Correct? Yes
Problem: Solve the following equation to find the value of r: 93 = ((19 * r) + 2)
GPT-4o:
To solve the equation \( 93 = (19r + 2) \) for \( r \), follow these steps:
1. Subtract 2 from both sides of the equation to isolate the term with \( r \):
\[
93 - 2 = 19r
\]
Simplifying the left side:
\[
91 = 19r
\]
2. Divide both sides by 19 to solve for \( r \):
\[
r = \frac{91}{19}
\]
Simplifying the fraction:
\[
r = 4.789
\]
### Answer: 4.789
Expected answer: 91/19
Correct? No
Problem: Solve the following linear equation for the value of z: 20 = (67 - (37 * z))
GPT-4o:
To solve the linear equation \( 20 = 67 - 37z \), we need to isolate the variable \( z \). Here are the steps:
1. Start with the given equation:
\[
20 = 67 - 37z
\]
2. Subtract 67 from both sides to move the constant term to the left side:
\[
20 - 67 = -37z
\]
3. Simplify the left side:
\[
-47 = -37z
\]
4. Divide both sides by -37 to solve for \( z \):
\[
z = \frac{-47}{-37}
\]
5. Simplify the fraction:
\[
z = \frac{47}{37}
\]
### Answer: \( \frac{47}{37} \)
Expected answer: 47/37
Correct? Yes
Problem: Solve the following linear equation for m: 65 = ((25 * m) + 15)
GPT-4o:
To solve the linear equation for \( m \):
\[ 65 = 25m + 15 \]
First, isolate the term with \( m \) by subtracting 15 from both sides of the equation:
\[ 65 - 15 = 25m \]
This simplifies to:
\[ 50 = 25m \]
Next, solve for \( m \) by dividing both sides by 25:
\[ m = \frac{50}{25} \]
This simplifies to:
\[ m = 2 \]
### Answer: 2
Expected answer: 2
Correct? Yes
Problem: Solve the following linear equation for g: 79 = ((6 * g) + 19)
GPT-4o:
To solve the linear equation \( 79 = 6g + 19 \) for \( g \), follow these steps:
1. Subtract 19 from both sides of the equation to isolate the term with \( g \):
\[
79 - 19 = 6g
\]
Simplifying the left side:
\[
60 = 6g
\]
2. Divide both sides by 6 to solve for \( g \):
\[
\frac{60}{6} = g
\]
Simplifying the right side:
\[
g = 10
\]
### Answer: 10
Expected answer: 10
Correct? Yes
Problem: Solve the following linear equation for the variable 'l': 30 = ((56 * l) - 45)
GPT-4o:
To solve the linear equation \( 30 = 56l - 45 \) for the variable \( l \), follow these steps:
1. Start by isolating the term containing \( l \). Add 45 to both sides of the equation:
\[
30 + 45 = 56l - 45 + 45
\]
Simplifying the left side:
\[
75 = 56l
\]
2. Next, solve for \( l \) by dividing both sides of the equation by 56:
\[
l = \frac{75}{56}
\]
3. Simplify the fraction if possible. In this case, 75 and 56 have no common factors other than 1, so the fraction is already in its simplest form:
\[
l = \frac{75}{56}
\]
### Answer: \(\frac{75}{56}\)
Expected answer: 75/56
Correct? Yes
Problem: Solve the following equation to find the value of j: 57 = ((11 * j) + 4)
GPT-4o:
To solve the equation \( 57 = 11j + 4 \) for \( j \), follow these steps:
1. Subtract 4 from both sides of the equation to isolate the term with \( j \):
\[
57 - 4 = 11j
\]
\[
53 = 11j
\]
2. Divide both sides by 11 to solve for \( j \):
\[
j = \frac{53}{11}
\]
3. Simplify the fraction if possible:
\[
j = 4.8181\ldots \approx 4.818
\]
### Answer: 4.818
Expected answer: 53/11
Correct? No
Problem: Solve the following equation to find the value of 'f': 36 = 34 * f - 56
GPT-4o:
To solve the equation \( 36 = 34f - 56 \) for \( f \), follow these steps:
1. Add 56 to both sides of the equation to isolate the term with \( f \) on one side:
\[
36 + 56 = 34f - 56 + 56
\]
Simplifying this, we get:
\[
92 = 34f
\]
2. Divide both sides of the equation by 34 to solve for \( f \):
\[
f = \frac{92}{34}
\]
3. Simplify the fraction:
\[
f = \frac{92}{34} = \frac{46}{17} = 2.7
\]
### Answer: 2.7
Expected answer: 46/17
Correct? No
Problem: Solve the following linear equation to find the value of 'u': 56 = (70 * u) - 43
GPT-4o:
To solve the linear equation \( 56 = 70u - 43 \), we need to isolate the variable \( u \). Here are the steps:
1. Start with the given equation:
\[
56 = 70u - 43
\]
2. Add 43 to both sides of the equation to move the constant term on the right side to the left side:
\[
56 + 43 = 70u
\]
3. Simplify the left side:
\[
99 = 70u
\]
4. Divide both sides by 70 to solve for \( u \):
\[
u = \frac{99}{70}
\]
5. Simplify the fraction if possible:
\[
u = \frac{99}{70} = 1.4142857142857143 \approx 1.414
\]
### Answer: \( \frac{99}{70} \) or approximately 1.414
Expected answer: 99/70
Correct? Yes
Problem: Solve the following equation for the variable x: 67 = 21 + 9*x
GPT-4o:
To solve the equation \( 67 = 21 + 9x \) for the variable \( x \), follow these steps:
1. Subtract 21 from both sides of the equation to isolate the term with \( x \):
\[
67 - 21 = 9x
\]
2. Simplify the left side:
\[
46 = 9x
\]
3. Divide both sides by 9 to solve for \( x \):
\[
x = \frac{46}{9}
\]
4. Simplify the fraction if possible. In this case, \(\frac{46}{9}\) is already in its simplest form.
### Answer: \( \frac{46}{9} \)
Expected answer: 46/9
Correct? Yes
Problem: Determine the unknown variable in the following equation: 75 = (58 + 16 * i)
GPT-4o:
To determine the unknown variable \( i \) in the equation \( 75 = 58 + 16i \), we need to isolate \( i \).
First, subtract 58 from both sides of the equation:
\[ 75 - 58 = 16i \]
Simplify the left side:
\[ 17 = 16i \]
Next, divide both sides by 16 to solve for \( i \):
\[ i = \frac{17}{16} \]
### Answer: \(\frac{17}{16}\)
Expected answer: 17/16
Correct? Yes
Problem: Solve for x in the following equation: 111 = (54 + (39 * x))
GPT-4o:
To solve for \( x \) in the equation \( 111 = 54 + 39x \), follow these steps:
1. Subtract 54 from both sides of the equation to isolate the term with \( x \):
\[
111 - 54 = 39x
\]
2. Simplify the left side:
\[
57 = 39x
\]
3. Divide both sides by 39 to solve for \( x \):
\[
x = \frac{57}{39}
\]
4. Simplify the fraction:
\[
x = \frac{57 \div 3}{39 \div 3} = \frac{19}{13}
\]
### Answer: \( \frac{19}{13} \)
Expected answer: 19/13
Correct? Yes
Problem: Solve the following equation to find the value of 'o': 155 = ((26 * o) + 68)
GPT-4o:
To solve the equation \( 155 = 26o + 68 \) for \( o \), follow these steps:
1. Subtract 68 from both sides of the equation to isolate the term with \( o \):
\[
155 - 68 = 26o
\]
2. Calculate the left-hand side:
\[
87 = 26o
\]
3. Divide both sides by 26 to solve for \( o \):
\[
o = \frac{87}{26}
\]
4. Simplify the fraction:
\[
o = \frac{87}{26} = 3.346153846153846
\]
### Answer: 3.346153846153846
Expected answer: 87/26
Correct? No
Problem: Solve for p in the following equation: 7 = ((12 * p) - 17)
GPT-4o:
To solve for \( p \) in the equation \( 7 = 12p - 17 \), follow these steps:
1. Start with the given equation:
\[
7 = 12p - 17
\]
2. Add 17 to both sides of the equation to isolate the term with \( p \):
\[
7 + 17 = 12p - 17 + 17
\]
Simplifying the left side:
\[
24 = 12p
\]
3. Divide both sides by 12 to solve for \( p \):
\[
\frac{24}{12} = \frac{12p}{12}
\]
Simplifying both sides:
\[
2 = p
\]
### 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?
GPT-4o:
To find the value of the variable \( b \) in the equation \( 163 = 93 + 55b \), we need to isolate \( b \). Here are the steps:
1. Start with the given equation:
\[
163 = 93 + 55b
\]
2. Subtract 93 from both sides to isolate the term with \( b \):
\[
163 - 93 = 55b
\]
3. Simplify the left side:
\[
70 = 55b
\]
4. Divide both sides by 55 to solve for \( b \):
\[
b = \frac{70}{55}
\]
5. Simplify the fraction:
\[
b = \frac{14}{11}
\]
### Answer: \(\frac{14}{11}\)
Expected answer: 14/11
Correct? Yes
Problem: Solve the linear equation for the value of 'u': 62 = (u - 26)
GPT-4o:
To solve the linear equation for the value of \( u \), we start with the given equation: \[ 62 = u - 26 \] To isolate \( u \), we need to get rid of the \(-26\) on the right side. We do this by adding 26 to both sides of the equation: \[ 62 + 26 = u - 26 + 26 \] Simplifying both sides, we get: \[ 88 = u \] Thus, the value of \( u \) is: ### Answer: 88
Expected answer: 88
Correct? Yes
Problem: Solve the following equation for the variable a: 179 = ((63 * a) + 93)
GPT-4o:
To solve the equation for the variable \( a \):
\[ 179 = 63a + 93 \]
First, isolate the term containing \( a \) by subtracting 93 from both sides of the equation:
\[ 179 - 93 = 63a \]
Simplify the left side:
\[ 86 = 63a \]
Next, solve for \( a \) by dividing both sides by 63:
\[ a = \frac{86}{63} \]
Simplify the fraction if possible:
\[ a = \frac{86}{63} \]
Since 86 and 63 have no common factors other than 1, the fraction is already in its simplest form.
### Answer: \( \frac{86}{63} \)
Expected answer: 86/63
Correct? Yes
Problem: Find the value of c in the equation: 51 = ((27 * c) - 11)
GPT-4o:
To find the value of \( c \) in the equation \( 51 = (27c - 11) \), we need to isolate \( c \). Here are the steps:
1. Start with the given equation:
\[
51 = 27c - 11
\]
2. Add 11 to both sides to move the constant term on the right side to the left side:
\[
51 + 11 = 27c
\]
3. Simplify the left side:
\[
62 = 27c
\]
4. Divide both sides by 27 to solve for \( c \):
\[
c = \frac{62}{27}
\]
5. Simplify the fraction if possible. In this case, \( \frac{62}{27} \) is already in its simplest form.
### Answer: \(\frac{62}{27}\)
Expected answer: 62/27
Correct? Yes
Problem: Solve the following equation for 'd': 19 = ((28 * d) - 18)
GPT-4o:
To solve the equation for \( d \), we start with the given equation:
\[ 19 = (28d - 18) \]
First, we need to isolate the term containing \( d \). We do this by adding 18 to both sides of the equation:
\[ 19 + 18 = 28d \]
Simplifying the left side:
\[ 37 = 28d \]
Next, we solve for \( d \) by dividing both sides by 28:
\[ d = \frac{37}{28} \]
Simplifying the fraction, we get:
\[ d = \frac{37}{28} \]
### Answer: \(\frac{37}{28}\)
Expected answer: 37/28
Correct? Yes
Problem: Solve the following linear equation for the value of e: 159 = ((47 * e) + 62)
GPT-4o:
To solve the linear equation \( 159 = 47e + 62 \) for \( e \), follow these steps:
1. Subtract 62 from both sides of the equation to isolate the term with \( e \):
\[
159 - 62 = 47e
\]
2. Simplify the left side:
\[
97 = 47e
\]
3. Divide both sides by 47 to solve for \( e \):
\[
e = \frac{97}{47}
\]
4. Simplify the fraction if possible. In this case, 97 and 47 are both prime numbers, so the fraction is already in its simplest form:
\[
e = \frac{97}{47}
\]
### Answer: \(\frac{97}{47}\)
Expected answer: 97/47
Correct? Yes
Problem: Solve the following linear equation for the variable g: 145 = (50 + (91 * g))
GPT-4o:
To solve the linear equation for the variable \( g \):
\[ 145 = 50 + 91g \]
First, isolate the term containing \( g \) by subtracting 50 from both sides of the equation:
\[ 145 - 50 = 91g \]
This simplifies to:
\[ 95 = 91g \]
Next, solve for \( g \) by dividing both sides of the equation by 91:
\[ g = \frac{95}{91} \]
Simplify the fraction if possible:
\[ g = \frac{95}{91} = \frac{95 \div 5}{91 \div 5} = \frac{19}{18.2} \]
Since 95 and 91 do not have a common factor other than 1, the fraction is already in its simplest form.
### Answer: \(\frac{95}{91}\)
Expected answer: 95/91
Correct? Yes
Problem: Solve the following linear equation for the value of l: 123 = ((44 * l) + 73)
GPT-4o:
To solve the linear equation \( 123 = 44l + 73 \) for \( l \), follow these steps:
1. Subtract 73 from both sides of the equation to isolate the term with \( l \):
\[
123 - 73 = 44l
\]
2. Simplify the left side:
\[
50 = 44l
\]
3. Divide both sides by 44 to solve for \( l \):
\[
l = \frac{50}{44}
\]
4. Simplify the fraction:
\[
l = \frac{25}{22}
\]
### Answer: \(\frac{25}{22}\)
Expected answer: 25/22
Correct? Yes
Problem: Solve the following equation: 165 = ((19 * q) + 75)
GPT-4o:
To solve the equation \( 165 = 19q + 75 \), we need to isolate the variable \( q \).
1. Subtract 75 from both sides of the equation:
\[
165 - 75 = 19q
\]
Simplifying the left side:
\[
90 = 19q
\]
2. Divide both sides by 19 to solve for \( q \):
\[
q = \frac{90}{19}
\]
3. Simplify the fraction:
\[
q = \frac{90}{19} \approx 4.7368
\]
### Answer: \( \frac{90}{19} \) or approximately 4.7368
Expected answer: 90/19
Correct? Yes
Problem: Solve the following linear equation to find the value of g: 149 = ((18 * g) + 62)
GPT-4o:
To solve the linear equation \( 149 = 18g + 62 \), we need to isolate the variable \( g \). Here are the steps:
1. Subtract 62 from both sides of the equation to get rid of the constant term on the right side:
\[
149 - 62 = 18g
\]
2. Simplify the left side:
\[
87 = 18g
\]
3. Divide both sides by 18 to solve for \( g \):
\[
g = \frac{87}{18}
\]
4. Simplify the fraction:
\[
g = \frac{87 \div 3}{18 \div 3} = \frac{29}{6}
\]
So, the value of \( g \) is:
### Answer: \(\frac{29}{6}\)
Expected answer: 29/6
Correct? Yes
Problem: Solve the following linear equation for the variable d: 84 = 20 * d + 21
GPT-4o:
To solve the linear equation \( 84 = 20d + 21 \) for the variable \( d \), follow these steps:
1. Subtract 21 from both sides of the equation to isolate the term with \( d \):
\[
84 - 21 = 20d + 21 - 21
\]
Simplifying this, we get:
\[
63 = 20d
\]
2. Divide both sides of the equation by 20 to solve for \( d \):
\[
\frac{63}{20} = d
\]
Thus, the value of \( d \) is:
### Answer: \(\frac{63}{20}\)
Expected answer: 63/20
Correct? Yes
Problem: Solve the following equation to find the value of g: 61 = (50 + (6 * g))
GPT-4o:
To solve the equation \( 61 = 50 + 6g \), we need to isolate the variable \( g \).
1. Start by subtracting 50 from both sides of the equation:
\[
61 - 50 = 50 + 6g - 50
\]
Simplifying this, we get:
\[
11 = 6g
\]
2. Next, divide both sides by 6 to solve for \( g \):
\[
\frac{11}{6} = g
\]
So, the value of \( g \) is:
### Answer: \(\frac{11}{6}\)
Expected answer: 11/6
Correct? Yes
Problem: Solve the following linear equation for the unknown variable v: 126 = ((21 * v) + 76)
GPT-4o:
To solve the linear equation for the unknown variable \( v \), we start with the given equation:
\[ 126 = 21v + 76 \]
First, we need to isolate the term containing \( v \). We do this by subtracting 76 from both sides of the equation:
\[ 126 - 76 = 21v \]
Simplifying the left side:
\[ 50 = 21v \]
Next, we solve for \( v \) by dividing both sides of the equation by 21:
\[ v = \frac{50}{21} \]
Thus, the value of \( v \) is:
### Answer: \(\frac{50}{21}\)
Expected answer: 50/21
Correct? Yes
Problem: Solve the following linear equation for g: 74 = ((91 * g) - 24)
GPT-4o:
To solve the linear equation for \( g \), we start with the given equation:
\[ 74 = 91g - 24 \]
First, we need to isolate the term containing \( g \). We do this by adding 24 to both sides of the equation:
\[ 74 + 24 = 91g - 24 + 24 \]
This simplifies to:
\[ 98 = 91g \]
Next, we solve for \( g \) by dividing both sides of the equation by 91:
\[ g = \frac{98}{91} \]
Simplify the fraction:
\[ g = \frac{98 \div 7}{91 \div 7} = \frac{14}{13} \]
### Answer: \(\frac{14}{13}\)
Expected answer: 14/13
Correct? Yes