Let's analyze each of the equations to determine their solution sets.
### Equation A:
\[ 3(4 - 5h) - 7 = -12 + 2h \]
First, we'll simplify the left-hand side:
1. Distribute:
\[ 3(4) - 3(5h) - 7 = -12 + 2h \]
\[ 12 - 15h - 7 = -12 + 2h \]
2. Combine like terms:
\[ 5 - 15h = -12 + 2h \]
3. Add \(15h\) to both sides:
\[ 5 = -12 + 17h \]
4. Add \(12\) to both sides:
\[ 17 = 17h \]
5. Divide by \(17\):
\[ h = 1 \]
So, the solution for Equation A is \( h = 1 \).
---
### Equation B:
\[ 2(p - 3) - 1 = 6p + \frac{14}{2} \]
We'll simplify the left-hand side as follows:
1. Distribute:
\[ 2p - 6 - 1 = 6p + 7 \]
2. Combine like terms:
\[ 2p - 7 = 6p + 7 \]
3. Subtract \(2p\) from both sides:
\[ -7 = 4p + 7 \]
4. Subtract \(7\) from both sides:
\[ -14 = 4p \]
5. Divide by \(4\):
\[ p = -\frac{14}{4} \]
\[ p = -\frac{7}{2} \]
So, the solution for Equation B is \( p = -\frac{7}{2} \).
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### Equation C:
\[ \frac{2}{3}v - 3 + \frac{8}{3} = -1 \]
Combine like terms on the left-hand side:
1. Convert \(-3\) to a fraction:
\[ -3 = -\frac{9}{3} \]
So the equation is:
\[ \frac{2}{3}v - \frac{9}{3} + \frac{8}{3} = -1 \]
2. Combine the constants:
\[ \frac{2}{3}v - \frac{1}{3} = -1 \]
3. Add \(\frac{1}{3}\) to both sides:
\[ \frac{2}{3}v = -1 + \frac{1}{3} \]
Convert \(-1\) into thirds:
\[ -1 = -\frac{3}{3} \]
Therefore:
\[ \frac{2}{3}v = -\frac{3}{3} + \frac{1}{3} = -\frac{2}{3} \]
4. Multiply by \(\frac{3}{2}\):
\[ v = -1 \]
So, the solution for Equation C is \( v = -1 \).
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### Summary of Solutions:
- **Equation : \( h = 1 \)
- **Equation B**: \( p = -\frac{7}{2} \)
- **Equation C**: \( v = -1 \)
### Conclusion:
- **Tamara**: Incorrect (A and C have different solutions)
- **Payton**: Incorrect (B and C have different solutions)
- **Krish**: Incorrect (All three have different solutions)
- **Haruki**: Correct (None of the equations have the same solution)
Thus, Haruki is the one who is correct.