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

Krish
Krish

Haruki
Haruki

Payton
Payton

Tamara

Answer 1

Let's solve each equation to determine their solution sets.

Equation A: \[ 3(4 - 5h) - 7 = -12 + 2h \] First, distribute the 3: \[ 12 - 15h - 7 = -12 + 2h \] Combine like terms: \[ 5 - 15h = -12 + 2h \] Add 15h to both sides: \[ 5 = -12 + 17h \] Add 12 to both sides: \[ 17 = 17h \] Divide by 17: \[ h = 1 \]

Equation B: \[ 2(p - 3) - 1 = 6p + 142 \] Distribute the 2: \[ 2p - 6 - 1 = 6p + 142 \] Combine like terms: \[ 2p - 7 = 6p + 142 \] Subtract 2p from both sides: \[ -7 = 4p + 142 \] Subtract 142 from both sides: \[ -149 = 4p \] Divide by 4: \[ p = -\frac{149}{4} \]

Equation C: \[ 23v - 3 + 83 = -1 \] Combine like terms: \[ 23v + 80 = -1 \] Subtract 80 from both sides: \[ 23v = -81 \] Divide by 23: \[ v = -\frac{81}{23} \]

Now that we have the solutions:

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

Now let's analyze the claims:

1. Tamara claims A and C have the same solution (False).
2. Payton claims B and C have the same solution (False).
3. Krish claims all three have the same solution (False).
4. Haruki claims none of the equations have the same solution (True).

Based on our calculations, the only correct statement is Haruki's claim that none of the equations have the same solution.

The correct answer is Haruki.