Question

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