To identify who is correct about the solution sets of the linear equations, we will solve each equation one by one.
Equation A: \[ 3(4-5h) - 7 = -12 + 2h \]
Expanding the left side: \[ 12 - 15h - 7 = -12 + 2h \] \[ 5 - 15h = -12 + 2h \]
Now, rearranging gives: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \]
Solving for \( h \): \[ h = 1 \]
Equation B: \[ 2(p-3) - 1 = 6p + 142 \]
Expanding the left side: \[ 2p - 6 - 1 = 6p + 142 \] \[ 2p - 7 = 6p + 142 \]
Now, rearranging: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \]
Solving for \( p \): \[ p = -\frac{149}{4} \]
Equation C: \[ 23v - 3 + 83 = -1 \] \[ 23v + 80 = -1 \]
Now, rearranging gives: \[ 23v = -1 - 80 \] \[ 23v = -81 \]
Solving for \( v \): \[ v = -\frac{81}{23} \]
Now we can summarize the solutions:
- 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 let's analyze the claims:
- Tamara says Equation A and Equation C have the same solution. (False)
- Payton says Equation B and Equation C have the same solution. (False)
- Krish says all three have the same solution. (False)
- Haruki says that none of the equations have the same solution. (True)
In conclusion, the correct answer is Haruki.
1 answer