Question

Linear Expressions, Equations & Inequalities Unit Test
13 of 1513 of 15 Items





Question
Solve for x
to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6
(1 point)

Answer 1

To solve the equation \( 5(2x+2)-4=2x+6 \), let's first simplify both sides.

1. Distribute on the left side:

\[
5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6
\]

So the equation becomes:

\[
10x + 6 = 2x + 6
\]

2. Next, we can subtract \( 2x \) from both sides:

\[
10x - 2x + 6 = 6
\]

This simplifies to:

\[
8x + 6 = 6
\]

3. Now, subtract 6 from both sides:

\[
8x = 0
\]

4. Finally, divide both sides by 8:

\[
x = 0
\]

Since we have found a specific value for \( x \), the equation has **one solution**.

Therefore, the solution to the equation is \( x = 0 \).