Match the equation with the correct solution.(4 points)

Question

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 \( 7x - 2 = 4x + 13 \))