Question

Solve to determine if the equation has one, none, or infinate solutions
5(2x+2)-4=2x+6

Answer 1

To determine the number of solutions for the equation \( 5(2x + 2) - 4 = 2x + 6 \), we'll start by simplifying both sides of the equation.

1. Distribute the 5 on the left side:
\[
5(2x + 2) = 10x + 10
\]
So, the equation becomes:
\[
10x + 10 - 4 = 2x + 6
\]

2. Simplify the left side further:
\[
10x + 6 = 2x + 6
\]

3. Now, subtract \( 2x \) from both sides:
\[
10x - 2x + 6 = 6
\]
This simplifies to:
\[
8x + 6 = 6
\]

4. Next, subtract 6 from both sides:
\[
8x = 0
\]

5. Finally, divide by 8:
\[
x = 0
\]

Since we found a single solution \( x = 0 \), the equation has **one solution**.