Tamara, Payton, Krish, and Haruki are analyzing the solution sets to the following linear equations. Tamara says that Equation A and Equation C have the same solution. Payton says Equation B and Equation C have the same solution. Krish says all three have the same solution. Haruki says that none of the equations have the same solution. Identify who is correct about the linear equations.

Question

Equation A: 3(4−5h)−7=−12+2h

Equation B: 2(p−3)−1=6p+142

Equation C: 23v−3+83=−1

(1 point)
Responses

Haruki
Haruki

Payton
Payton

Tamara
Tamara

Krish
Krish
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Answer 1

To determine who is correct about the solution sets of the given equations, we will solve each equation step by step.

Equation A: \(3(4 - 5h) - 7 = -12 + 2h\)

1. Distributing: \(12 - 15h - 7 = -12 + 2h\)

2. Simplifying: \(5 - 15h = -12 + 2h\)

3. Moving terms involving \(h\) to one side and constants to the other: \(5 + 12 = 15h + 2h\) \(17 = 17h\)

4. Dividing both sides by 17: \(h = 1\)

Solution for Equation A: \(h = 1\)

Equation B: \(2(p - 3) - 1 = 6p + 142\)

1. Distributing: \(2p - 6 - 1 = 6p + 142\)

2. Simplifying: \(2p - 7 = 6p + 142\)

3. Reorganizing: \(-7 - 142 = 6p - 2p\) \(-149 = 4p\)

4. Dividing both sides by 4: \(p = -\frac{149}{4}\)

Solution for Equation B: \(p = -\frac{149}{4}\)

Equation C: \(23v - 3 + 83 = -1\)

1. Combining like terms: \(23v + 80 = -1\)

2. Moving 80 to the other side: \(23v = -1 - 80\) \(23v = -81\)

3. 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