Use drag and drop to place the two equations below that have the same solution.

Question

_______ has the same solution as ________.
A) x/2 + 4 = 5x - 10
B) 5x/9 = 3
C) 6x - 10 = 50
D) 2(5x + 4) = 8x + 28

Answer 1

To determine which equations have the same solution, we need to solve each equation for \( x \).

Equation A: \( \frac{x}{2} + 4 = 5x - 10 \)

1. Multiply through by 2 to eliminate the fraction: \[ x + 8 = 10x - 20 \]
2. Rearranging gives: \[ 8 + 20 = 10x - x \] \[ 28 = 9x \]
3. Solving for \( x \): \[ x = \frac{28}{9} \]

Equation B: \( \frac{5x}{9} = 3 \)

1. Multiply through by 9 to eliminate the fraction: \[ 5x = 27 \]
2. Solving for \( x \): \[ x = \frac{27}{5} \]

Equation C: \( 6x - 10 = 50 \)

1. Add 10 to both sides: \[ 6x = 60 \]
2. Solving for \( x \): \[ x = 10 \]

Equation D: \( 2(5x + 4) = 8x + 28 \)

1. Distribute the 2: \[ 10x + 8 = 8x + 28 \]
2. Rearranging gives: \[ 10x - 8x = 28 - 8 \] \[ 2x = 20 \]
3. Solving for \( x \): \[ x = 10 \]

Comparing Solutions:

• Equation A: \( x = \frac{28}{9} \)
• Equation B: \( x = \frac{27}{5} \)
• Equation C: \( x = 10 \)
• Equation D: \( x = 10 \)

Conclusion: Equations C and D have the same solution.

So, the correct matches are: _______ has the same solution as ________. C) 6x - 10 = 50 has the same solution as D) 2(5x + 4) = 8x + 28.