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Bot GPT 4-o mini Let's analyze each equation to determine the solution set for each one.
### Equation A:
\[ 3(4 - 5h) - 7 = -12 + 2h \]
First, simplify the left side:
\[ 12 - 15h - 7 = -12 + 2h \]
\[ 5 - 15h = -12 + 2h \]
Now, combine like terms:
\[ 5 + 12 = 15h + 2h \]
\[ 17 = 17h \]
Divide both sides by 17:
\[ h = 1 \]
### Equation B:
\[ 2(p - 3) - 1 = \frac{6p + 14}{2} \]
First, simplify the left side:
\[ 2p - 6 - 1 = \frac{6p + 14}{2} \]
\[ 2p - 7 = 3p + 7 \]
Now, combine like terms:
\[ 2p - 3p = 7 + 7 \]
\[ -p = 14 \]
Multiply both sides by -1:
\[ p = -14 \]
### Equation C:
\[ \frac{2}{3}v - 3 + \frac{8}{3} = -1 \]
First, combine the constants:
\[ \frac{2}{3}v - 3 + \frac{8}{3} = -1 \]
Convert -3 to a fraction with a denominator of 3:
\[ \frac{2}{3}v - \frac{9}{3} + \frac{8}{3} = -1 \]
Combine the constants:
\[ \frac{2}{3}v - \frac{1}{3} = -1 \]
Now, add \(\frac{1}{3}\) to both sides:
\[ \frac{2}{3}v = -1 + \frac{1}{3} \]
Convert -1 to a fraction with a denominator of 3:
\[ \frac{2}{3}v = -\frac{3}{3} + \frac{1}{3} \]
Combine the constants:
\[ \frac{2}{3}v = -\frac{2}{3} \]
Multiply both sides by \(\frac{3}{2}\):
\[ v = -1 \]
### Summary of Solutions:
- **Equation : \( h = 1 \)
- **Equation B**: \( p = -14 \)
- **Equation C**: \( v = -1 \)
Now let's evaluate the claims:
- **Tamara** claims that Equation A and Equation C have the same solution. Incorrect.
- **Payton** claims that Equation B and Equation C have the same solution. Incorrect.
- **Krish** claims that all three have the same solution. Incorrect.
- **Haruki** claims that none of the equations have the same solution. Correct.
Thus, **Haruki is correct**: none of the equations have the same solution.