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 solution. Krish 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.

Let's analyze each equation:

Equation A: \[ 3(4 - 5h) - 7 = -12 + 2h \]

First, simplify the left side: \[ 3(4) - 3(5h) - 7 = 12 - 15h - 7 = 5 - 15h \] Now simplify the right side: \[ -12 + 2h \] Now, set the two sides equal: \[ 5 - 15h = -12 + 2h \] Add \(15h\) to both sides: \[ 5 = -12 + 17h \] Add \(12\) to both sides: \[ 17 = 17h \] Divide by \(17\): \[ h = 1 \]

Equation B: \[ 2(p - 3) - 1 = 6p + 14 \]

Simplify the left side: \[ 2p - 6 - 1 = 2p - 7 \] Set the two sides equal: \[ 2p - 7 = 6p + 14 \] Subtract \(2p\) from both sides: \[ -7 = 4p + 14 \] Subtract \(14\) from both sides: \[ -21 = 4p \] Divide by \(4\): \[ p = -\frac{21}{4} \]

Equation C: From your writing, Equation C seems unclear, I will assume it's meant to be a different equation. Please provide the correct form of Equation C if it differs; however, to proceed with the assumption, I'll solve it as:

Assuming Equation C: \[ 0 - 3 + 8 = -1 \]

Which simplifies to: \[ 8 - 3 = -1 \text{ (This is incorrect)} \] This equation does not hold true, so I could not find a solution here.

To summarize:

• Equation A has a solution \(h = 1\).
• Equation B has a solution \(p = -\frac{21}{4}\).
• Equation C does not have a solution.

Final Verification of Claims:

• Tamara says A and C are the same: Incorrect.
• Payton says B and C are the same: Incorrect.
• Krish says all three are the same: Incorrect.
• Haruki says none have the same solution: Correct.

Thus, Haruki is the only correct person regarding the linear equations.