To determine who is correct, we need to solve each equation and find their respective solution sets.
Equation A: \[ 3(4-5h) - 7 = -12 + 2h \]
First, distribute: \[ 12 - 15h - 7 = -12 + 2h \] Simplify: \[ 5 - 15h = -12 + 2h \] Add \( 15h \) and \( 12 \) to both sides: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \] Divide both sides by 17: \[ h = 1 \]
Solution set for Equation A: \( h = 1 \)
Equation B: \[ 2(p-3) - 1 = 6p + 142 \]
Distribute: \[ 2p - 6 - 1 = 6p + 142 \] Combine like terms: \[ 2p - 7 = 6p + 142 \] Subtract \( 2p \) from both sides: \[ -7 = 6p - 2p + 142 \] \[ -7 = 4p + 142 \] Subtract 142 from both sides: \[ -7 - 142 = 4p \] \[ -149 = 4p \] Divide both sides by 4: \[ p = -\frac{149}{4} \]
Solution set for Equation B: \( p = -\frac{149}{4} \)
Equation C: \[ 23v - 3 + 83 = -1 \]
Combine like terms: \[ 23v + 80 = -1 \] Subtract 80 from both sides: \[ 23v = -1 - 80 \] \[ 23v = -81 \] Divide both sides by 23: \[ v = -\frac{81}{23} \]
Solution set for Equation C: \( v = -\frac{81}{23} \)
Now let's summarize the solutions:
- Equation A: \( h = 1 \)
- Equation B: \( p = -\frac{149}{4} \)
- Equation C: \( v = -\frac{81}{23} \)
Now let's evaluate the claims:
- Tamara: Claims Equation A and Equation C have the same solution. (Incorrect)
- Payton: Claims Equation B and Equation C have the same solution. (Incorrect)
- Krish: Claims all three have the same solution. (Incorrect)
- Haruki: Claims that none of the equations have the same solution. (Correct)
Final answer: Haruki is correct.