To determine who is correct about the solution sets of the given equations, we will solve each equation step by step.
Equation A: \[ 3(4 - 5h) - 7 = -12 + 2h \] Expanding and simplifying: \[ 12 - 15h - 7 = -12 + 2h \] \[ 5 - 15h = -12 + 2h \] Now, let's get all terms involving \( h \) on one side and constants on the other: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \] Dividing by 17: \[ h = 1 \]
Equation B: \[ 2(p - 3) - 1 = 6p + 142 \] Expanding: \[ 2p - 6 - 1 = 6p + 142 \] \[ 2p - 7 = 6p + 142 \] Rearranging: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \] Dividing by -4: \[ p = -\frac{149}{4} \]
Equation C: \[ 23v - 3 + 83 = -1 \] Combining like terms: \[ 23v + 80 = -1 \] Rearranging: \[ 23v = -1 - 80 \] \[ 23v = -81 \] Dividing by 23: \[ v = -\frac{81}{23} \]
Now we have the solutions:
- For Equation A: \( h = 1 \)
- For Equation B: \( p = -\frac{149}{4} \)
- For Equation C: \( v = -\frac{81}{23} \)
Evaluating the claims:
- Tamara claims Equations A and C have the same solution. (This is false, since \( h \neq v \)).
- Payton claims Equations B and C have the same solution. (This is false, since \( p \neq v \)).
- Krish claims all three equations have the same solution. (This is false since none of the equations yield the same solution).
- Haruki claims none of the equations have the same solution. (This is true).
Thus, Haruki is correct.