To determine who is correct about the given linear equations, we need to solve each equation and identify their solution sets.
**Equation A:**
\[ 3(4 - 5h) - 7 = -12 + 2h \]
Distributing 3:
\[ 12 - 15h - 7 = -12 + 2h \]
Combining like terms:
\[ 5 - 15h = -12 + 2h \]
Adding 15h to both sides:
\[ 5 = -12 + 17h \]
Adding 12 to both sides:
\[ 17 = 17h \]
Dividing by 17:
\[ h = 1 \]
**Equation B:**
\[ 2(p - 3) - 1 = 6p + 142 \]
Distributing 2:
\[ 2p - 6 - 1 = 6p + 142 \]
Combining like terms:
\[ 2p - 7 = 6p + 142 \]
Subtracting 2p from both sides:
\[ -7 = 4p + 142 \]
Subtracting 142 from both sides:
\[ -149 = 4p \]
Dividing by 4:
\[ p = -\frac{149}{4} \]
**Equation C:**
\[ 23v - 3 + 83 = -1 \]
Combining terms:
\[ 23v + 80 = -1 \]
Subtracting 80 from both sides:
\[ 23v = -81 \]
Dividing by 23:
\[ v = -\frac{81}{23} \]
Now we have the solutions:
- **Equation has the solution \( h = 1 \).
- **Equation B** has the solution \( p = -\frac{149}{4} \).
- **Equation C** has the solution \( v = -\frac{81}{23} \).
Comparing the solutions:
- Equation A has a solution of \( h = 1 \).
- Equation B has a solution of \( p = -\frac{149}{4} \).
- Equation C has a solution of \( v = -\frac{81}{23} \).
Since all three equations yield different solutions, Haruki is correct in stating that none of the equations have the same solution.
**Final Answer: Haruki**