To determine who is correct about the solution sets of the linear equations, we need to solve each equation and find their solutions.
Equation A: \[ 3(4-5h) - 7 = -12 + 2h \] Expanding the left side: \[ 12 - 15h - 7 = -12 + 2h \] Combining like terms: \[ 5 - 15h = -12 + 2h \] Bringing all terms involving \(h\) to one side and constant terms to the other side: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \] Dividing both sides by 17: \[ h = 1 \]
Equation B: \[ 2(p-3) - 1 = \frac{6p + 14}{2} \] Multiplying both sides by 2 to eliminate the fraction: \[ 2(2(p-3) - 1) = 6p + 14 \] Expanding: \[ 4p - 6 - 2 = 6p + 14 \] Combining like terms: \[ 4p - 8 = 6p + 14 \] Bringing all terms involving \(p\) to one side: \[ 4p - 6p = 14 + 8 \] \[ -2p = 22 \] Dividing both sides by -2: \[ p = -11 \]
Equation C: \[ 23v - 3 + 83 = -1 \] Combining like terms: \[ 23v + 80 = -1 \] Bringing 80 to the other side: \[ 23v = -1 - 80 \] \[ 23v = -81 \] Dividing both sides by 23: \[ v = -\frac{81}{23} \]
Now we have:
- Equation A has solution \(h = 1\)
- Equation B has solution \(p = -11\)
- Equation C has solution \(v = -\frac{81}{23}\)
Based on these results:
- Tamara is incorrect (A and C do not have the same solution).
- Payton is incorrect (B and C do not have the same solution).
- Krish is incorrect (A, B, and C do not have the same solution).
- Haruki is correct (none of the equations have the same solution).
Thus, the correct answer is: Haruki.
1 answer