Let's analyze each equation to determine the solution set for each one.
Equation A:
\[ 3(4 - 5h) - 7 = -12 + 2h \]
First, simplify the left side: \[ 12 - 15h - 7 = -12 + 2h \] \[ 5 - 15h = -12 + 2h \] Now, combine like terms: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \] Divide both sides by 17: \[ h = 1 \]
Equation B:
\[ 2(p - 3) - 1 = \frac{6p + 14}{2} \]
First, simplify the left side: \[ 2p - 6 - 1 = \frac{6p + 14}{2} \] \[ 2p - 7 = 3p + 7 \] Now, combine like terms: \[ 2p - 3p = 7 + 7 \] \[ -p = 14 \] Multiply both sides by -1: \[ p = -14 \]
Equation C:
\[ \frac{2}{3}v - 3 + \frac{8}{3} = -1 \]
First, combine the constants: \[ \frac{2}{3}v - 3 + \frac{8}{3} = -1 \] Convert -3 to a fraction with a denominator of 3: \[ \frac{2}{3}v - \frac{9}{3} + \frac{8}{3} = -1 \] Combine the constants: \[ \frac{2}{3}v - \frac{1}{3} = -1 \]
Now, add \(\frac{1}{3}\) to both sides: \[ \frac{2}{3}v = -1 + \frac{1}{3} \] Convert -1 to a fraction with a denominator of 3: \[ \frac{2}{3}v = -\frac{3}{3} + \frac{1}{3} \] Combine the constants: \[ \frac{2}{3}v = -\frac{2}{3} \] Multiply both sides by \(\frac{3}{2}\): \[ v = -1 \]
Summary of Solutions:
- Equation A: \( h = 1 \)
- Equation B: \( p = -14 \)
- Equation C: \( v = -1 \)
Now let's evaluate the claims:
- Tamara claims that Equation A and Equation C have the same solution. Incorrect.
- Payton claims that Equation B and Equation C have the same solution. Incorrect.
- Krish claims that all three have the same solution. Incorrect.
- Haruki claims that none of the equations have the same solution. Correct.
Thus, Haruki is correct: none of the equations have the same solution.
1 answer