Tamara, Payton, Krish, and Haruki are analyzing the solution sets to the following linear equations Tamara says that Equation A and Equation C have the same solution Payton says Equation B and Equation C have the same solutionKrish says all three have the same solution Haruki says that none of the equations have the same solution Identify who is correct about the linear equations Equation A 3(4 - 5h) - 7 = - 12 + 2h Equation B 2(p - 3) - 1 = (6p + 14)/2 Equation 2/3 * v - 3 + 8/3 = - 1 (1 point ) Haruki Payton Tamara Krish

To determine who among Tamara, Payton, Krish, and Haruki is correct about the linear equations, let's solve each of the equations one by one.

### Equation A:
\[ 3(4 - 5h) - 7 = -12 + 2h \]
1. Distribute:
\[ 12 - 15h - 7 = -12 + 2h \]
2. Simplify:
\[ 5 - 15h = -12 + 2h \]
3. Rearranging gives:
\[ 5 + 12 = 15h + 2h \]
\[ 17 = 17h \]
4. Solving for h:
\[ h = 1 \]

### Equation B:
\[ 2(p - 3) - 1 = \frac{6p + 14}{2} \]
1. Distribute:
\[ 2p - 6 - 1 = 3p + 7 \]
2. Simplifying gives:
\[ 2p - 7 = 3p + 7 \]
3. Rearranging gives:
\[ -7 - 7 = 3p - 2p \]
\[ -14 = p \]
4. So, \( p = -14 \).

### Equation C:
\[ \frac{2}{3}v - 3 + \frac{8}{3} = -1 \]
1. Combine constants:
\[ \frac{2}{3}v + \frac{8}{3} - 3 = -1 \]
\[ \frac{2}{3}v + \frac{8 - 9}{3} = -1 \]
\[ \frac{2}{3}v - \frac{1}{3} = -1 \]
2. Adding \( \frac{1}{3} \):
\[ \frac{2}{3}v = -1 + \frac{1}{3} \]
\[ \frac{2}{3}v = -\frac{3}{3} + \frac{1}{3} \]
\[ \frac{2}{3}v = -\frac{2}{3} \]
3. Multiplying by \( \frac{3}{2} \):
\[ v = -1 \]

### Summary of Solutions:
- Equation A: \( h = 1 \)
- Equation B: \( p = -14 \)
- Equation C: \( v = -1 \)

### Analyzing the Claims:
1. Tamara (Equation A and Equation C have the same solution): **Incorrect**
- A: \( h = 1 \), C: \( v = -1 \) (different solutions)
2. Payton (Equation B and Equation C have the same solution): **Incorrect**
- B: \( p = -14 \), C: \( v = -1 \) (different solutions)
3. Krish (All three have the same solution): **Incorrect**
- All solutions are different.
4. Haruki (None of the equations have the same solution): **Correct**
- All three equations have different solutions.

**Final Answer:** Haruki is correct.