To determine who is correct about the solution sets of the given equations, we will solve each equation step by step.
Equation A: \(3(4 - 5h) - 7 = -12 + 2h\)
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Distributing: \(12 - 15h - 7 = -12 + 2h\)
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Simplifying: \(5 - 15h = -12 + 2h\)
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Moving terms involving \(h\) to one side and constants to the other: \(5 + 12 = 15h + 2h\) \(17 = 17h\)
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Dividing both sides by 17: \(h = 1\)
Solution for Equation A: \(h = 1\)
Equation B: \(2(p - 3) - 1 = 6p + 142\)
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Distributing: \(2p - 6 - 1 = 6p + 142\)
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Simplifying: \(2p - 7 = 6p + 142\)
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Reorganizing: \(-7 - 142 = 6p - 2p\) \(-149 = 4p\)
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Dividing both sides by 4: \(p = -\frac{149}{4}\)
Solution for Equation B: \(p = -\frac{149}{4}\)
Equation C: \(23v - 3 + 83 = -1\)
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Combining like terms: \(23v + 80 = -1\)
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Moving 80 to the other side: \(23v = -1 - 80\) \(23v = -81\)
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Dividing by 23: \(v = -\frac{81}{23}\)
Solution for Equation C: \(v = -\frac{81}{23}\)
Summary of Solutions:
- Equation A: \(h = 1\)
- Equation B: \(p = -\frac{149}{4}\)
- Equation C: \(v = -\frac{81}{23}\)
Now, Evaluating the Claims:
- Tamara said Equation A and Equation C have the same solution: Incorrect (1 ≠ -81/23)
- Payton said Equation B and Equation C have the same solution: Incorrect (-149/4 ≠ -81/23)
- Krish said all three have the same solution: Incorrect
- Haruki said that none of the equations have the same solution: Correct
Final Answer:
Haruki