To determine who is correct about the solution sets of the equations, I will solve each equation step-by-step:
Equation A: \[ 3(4 - 5h) - 7 = -12 + 2h \] First, distribute on the left side: \[ 12 - 15h - 7 = -12 + 2h \] Combine like terms: \[ 5 - 15h = -12 + 2h \] Now, move all terms involving \( h \) to one side and constant terms to the other: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \] Divide both sides by 17: \[ h = 1 \]
Equation B: \[ 2(p - 3) - 1 = 6p + 142 \] First, distribute on the left side: \[ 2p - 6 - 1 = 6p + 142 \] Combine like terms: \[ 2p - 7 = 6p + 142 \] Now, move all terms involving \( p \) to one side and constant terms to the other: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \] Divide both sides by 4: \[ p = -\frac{149}{4} \]
Equation C: \[ 23v - 3 + 83 = -1 \] Combine like terms on the left side: \[ 23v + 80 = -1 \] Move the constant to the right: \[ 23v = -1 - 80 \] \[ 23v = -81 \] Divide both sides by 23: \[ v = -\frac{81}{23} \]
Now, we summarize the solutions to each equation:
- Equation A: \( h = 1 \)
- Equation B: \( p = -\frac{149}{4} \)
- Equation C: \( v = -\frac{81}{23} \)
From the solutions:
- All three equations yield different values.
- This means that Tamara (who claims A and C are the same), Payton (who claims B and C are the same), Krish (who claims all three are the same), and Haruki (who claims none are the same) are incorrect about their specific claims.
The one who is correct is Haruki, as he states that none of the equations have the same solution.
Final response: Haruki
1 answer