To determine who is correct about the solution sets of the given equations, we need to solve each equation one by one.
Equation A:
\[ 3(4-5h) - 7 = -12 + 2h \]
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Distributing \(3\): \[ 12 - 15h - 7 = -12 + 2h \] \[ 5 - 15h = -12 + 2h \]
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Adding \(15h\) and \(12\) to both sides: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \]
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Dividing both sides by \(17\): \[ h = 1 \]
Equation B:
\[ 2(p-3) - 1 = 6p + 142 \]
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Distributing \(2\): \[ 2p - 6 - 1 = 6p + 142 \] \[ 2p - 7 = 6p + 142 \]
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Moving \(6p\) to the left side: \[ 2p - 6p = 142 + 7 \] \[ -4p = 149 \]
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Dividing both sides by \(-4\): \[ p = -\frac{149}{4} \]
Equation C:
\[ 23v - 3 + 83 = -1 \]
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Combine like terms: \[ 23v + 80 = -1 \]
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Moving \(80\) to the right side: \[ 23v = -1 - 80 \] \[ 23v = -81 \]
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Dividing both sides by \(23\): \[ v = -\frac{81}{23} \]
Summary of Solutions:
- From Equation A: \( h = 1 \)
- From Equation B: \( p = -\frac{149}{4} \)
- From Equation C: \( v = -\frac{81}{23} \)
Analyzing Statements:
- Tamara (Equation A and C have the same solution): Incorrect (Different solutions).
- Payton (Equation B and C have the same solution): Incorrect (Different solutions).
- Krish (All three have the same solution): Incorrect (All different).
- Haruki (None of the equations have the same solution): Correct.
Thus, Haruki is the only one who is correct.
1 answer