Let's solve each of the equations to determine their solution sets and identify who is correct.
### Equation A: \( 3(4−5h)−7=−12+2h \)
1. Distribute on the left side:
\[
3 \times 4 - 3 \times 5h - 7 = -12 + 2h
\]
\[
12 - 15h - 7 = -12 + 2h
\]
\[
5 - 15h = -12 + 2h
\]
2. Rearrange the equation:
\[
5 + 12 = 2h + 15h
\]
\[
17 = 17h
\]
3. Solve for \( h \):
\[
h = 1
\]
So the solution for Equation A is \( h = 1 \).
### Equation B: \( 2(p−3)−1=6p+\frac{14}{2} \)
1. Simplify \( \frac{14}{2} \):
\[
2(p - 3) - 1 = 6p + 7
\]
2. Distribute on the left side:
\[
2p - 6 - 1 = 6p + 7
\]
\[
2p - 7 = 6p + 7
\]
3. Rearrange the equation:
\[
2p - 6p = 7 + 7
\]
\[
-4p = 14
\]
4. Solve for \( p \):
\[
p = -\frac{14}{4} = -\frac{7}{2}
\]
So the solution for Equation B is \( p = -\frac{7}{2} \).
### Equation C: \( \frac{2}{3}v−3+\frac{8}{3}=−1 \)
1. Combine like terms:
\[
\frac{2}{3}v - 3 + \frac{8}{3} = -1
\]
\[
\frac{2}{3}v - 3 + \frac{8}{3} = -1
\]
\[
\frac{2}{3}v - 3 + 2.6667 = -1 \quad (as \, \frac{8}{3} = 2.6667)
\]
\[
\frac{2}{3}v - 0.3333 = -1
\]
2. Add 3:
\[
\frac{2}{3}v = -1 + 0.3333
\]
\[
\frac{2}{3}v = -0.6667
\]
3. Multiply both sides by \(\frac{3}{2}\):
\[
v = -0.6667 \frac{3}{2}
\]
\[
v = -1
\]
So the solution for Equation C is \( v = -1 \).
### Summary of Solutions
- Equation A: \( h = 1 \)
- Equation B: \( p = -\frac{7}{2} \)
- Equation C: \( v = -1 \)
Now we evaluate the claims:
- **Tamara**: Incorrect, because A and C have different solutions.
- **Payton**: Incorrect, because B and C have different solutions.
- **Krish**: Incorrect, because all equations have different solutions.
- **Haruki**: Correct, none of the equations have the same solution.
### Final Answer:
**Haruki** is correct.