Question

Match the equation with the correct solution.(4 points)
6x+4=10x−8
3x−5=2x+10
4x−3=2x+5
7x−2=4x+13
Responses: x=15 x=3 x=4 x=5

Answer 1

Let's solve each equation step by step and match them with the correct solutions.

1. **Equation:** \( 6x + 4 = 10x - 8 \)
**Solution:**
\( 6x + 4 = 10x - 8 \)
Rearranging gives us:
\( 4 + 8 = 10x - 6x \)
\( 12 = 4x \)
\( x = 3 \)

2. **Equation:** \( 3x - 5 = 2x + 10 \)
**Solution:**
\( 3x - 5 = 2x + 10 \)
Rearranging gives us:
\( 3x - 2x = 10 + 5 \)
\( x = 15 \)

3. **Equation:** \( 4x - 3 = 2x + 5 \)
**Solution:**
\( 4x - 3 = 2x + 5 \)
Rearranging gives us:
\( 4x - 2x = 5 + 3 \)
\( 2x = 8 \)
\( x = 4 \)

4. **Equation:** \( 7x - 2 = 4x + 13 \)
**Solution:**
\( 7x - 2 = 4x + 13 \)
Rearranging gives us:
\( 7x - 4x = 13 + 2 \)
\( 3x = 15 \)
\( x = 5 \)

**Final Matches:**
- \( 6x + 4 = 10x - 8 \) → \( x = 3 \)
- \( 3x - 5 = 2x + 10 \) → \( x = 15 \)
- \( 4x - 3 = 2x + 5 \) → \( x = 4 \)
- \( 7x - 2 = 4x + 13 \) → \( x = 5 \)

Responses:
- \( x = 3 \) (for \( 6x + 4 = 10x - 8 \))
- \( x = 15 \) (for \( 3x - 5 = 2x + 10 \))
- \( x = 4 \) (for \( 4x - 3 = 2x + 5 \))
- \( x = 5 \) (for \( 7x - 2 = 4x + 13 \))