Question

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. 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 Krish Krish Payton Payton Tamara

Answer 1

Let's solve each equation one by one to find their solution sets.

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

1. Distribute the left side: \[ 12 - 15h - 7 = -12 + 2h \] Simplifying gives: \[ 5 - 15h = -12 + 2h \]

2. Add \( 15h \) and \( 12 \) to both sides: \[ 5 + 12 = 15h + 2h \] Simplifying gives: \[ 17 = 17h \] So: \[ h = 1 \]

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

1. Distribute: \[ 2p - 6 - 1 = 6p + 142 \]

2. Simplify: \[ 2p - 7 = 6p + 142 \]

3. Rearranging gives: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \] So: \[ p = -\frac{149}{4} ; or ; -37.25 \]

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

1. Simplify the left side: \[ 23v + 80 = -1 \]

2. Rearranging gives: \[ 23v = -1 - 80 \] \[ 23v = -81 \] So: \[ v = -\frac{81}{23} \]

Summary of Solutions:

• Equation A has solution \( h = 1 \).
• Equation B has solution \( p = -\frac{149}{4} \).
• Equation C has solution \( v = -\frac{81}{23} \).

Now, let's analyze the claims made by Tamara, Payton, Krish, and Haruki:

• Tamara says Equation A and Equation C have the same solution. (False: \( h = 1 \) and \( v = -\frac{81}{23} \))
• Payton says Equation B and Equation C have the same solution. (False: \( p = -\frac{149}{4} \) and \( v = -\frac{81}{23} \))
• Krish says all three have the same solution. (False: all three have different solutions)
• Haruki says that none of the equations have the same solution. (True: all have different solutions)

Thus, the correct answer is Haruki.