To determine who is correct about the solution sets of the given equations, we need to solve each equation one by one.
Equation A:
\[
3(4 - 5h) - 7 = -12 + 2h
\]
Distributing the left side:
\[
12 - 15h - 7 = -12 + 2h
\]
This simplifies to:
\[
5 - 15h = -12 + 2h
\]
Now, move all terms involving \(h\) to one side and constant terms to the other side:
\[
5 + 12 = 15h + 2h
\]
\[
17 = 17h
\]
\[
h = 1
\]
Equation B: \[ 2(p - 3) - 1 = 6p + 142 \] Distributing the left side: \[ 2p - 6 - 1 = 6p + 142 \] Simplifying gives us: \[ 2p - 7 = 6p + 142 \] Rearranging terms: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \] \[ p = -\frac{149}{4} \]
Equation C: \[ 23v - 3 + 83 = -1 \] This simplifies to: \[ 23v + 80 = -1 \] Subtract 80 from both sides: \[ 23v = -1 - 80 \] \[ 23v = -81 \] \[ v = -\frac{81}{23} \]
Solution Summary:
- Equation A has the solution \(h = 1\)
- Equation B has the solution \(p = -\frac{149}{4}\)
- Equation C has the solution \(v = -\frac{81}{23}\)
Now, comparing the solutions:
- Tamara claims A and C have the same solution, which is incorrect.
- Payton claims B and C have the same solution, which is incorrect.
- Krish claims all three equations have the same solution, which is incorrect.
- Haruki claims none of the equations have the same solution, which is correct.
Therefore, the correct answer is:
Haruki
1 answer