To determine who is correct about the solutions of the equations, we'll first solve each equation and find their solutions.
Equation A: \[ 3(4 - 5h) - 7 = -12 + 2h \]
Distributing on the left side: \[ 12 - 15h - 7 = -12 + 2h \] \[ 5 - 15h = -12 + 2h \]
Bringing all terms involving \( h \) to one side and constants to the other: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \]
Dividing both sides by 17: \[ h = 1 \]
So, the solution for Equation A is \( h = 1 \).
Equation B: \[ 2(p - 3) - 1 = 6p + 142 \]
Distributing on the left side: \[ 2p - 6 - 1 = 6p + 142 \] \[ 2p - 7 = 6p + 142 \]
Rearranging gives: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \]
Dividing both sides by 4: \[ p = -\frac{149}{4} \]
So, the solution for Equation B is \( p = -\frac{149}{4} \).
Equation C: \[ 23v - 3 + 83 = -1 \] \[ 23v + 80 = -1 \]
Solving for \( v \): \[ 23v = -1 - 80 \] \[ 23v = -81 \]
Dividing both sides by 23: \[ v = -\frac{81}{23} \]
So, the solution for Equation C is \( v = -\frac{81}{23} \).
Now, we can compare the solutions:
- Solution for Equation A: \( h = 1 \)
- Solution for Equation B: \( p = -\frac{149}{4} \)
- Solution for Equation C: \( v = -\frac{81}{23} \)
Since \( 1 \), \( -\frac{149}{4} \), and \( -\frac{81}{23} \) are all distinct, it follows:
- 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 (not all three have the same solution).
- Haruki is correct (none of the equations have the same solution).
Thus, Haruki is the one who is correct.
1 answer