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)
Responses

The equation has one solution: x=1
.
The equation has one solution: x equals 1 .

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .

The equation has no solution.

Answer 1

To solve the equation \(5(2x+2)−4=2x+6\), let's simplify it step by step.

1. Start with the original equation:
\[
5(2x + 2) - 4 = 2x + 6
\]

2. Distribute \(5\) on the left side:
\[
10x + 10 - 4 = 2x + 6
\]
This simplifies to:
\[
10x + 6 = 2x + 6
\]

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

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

5. Finally, divide both sides by \(8\):
\[
x = 0
\]

Now, let's consider the number of solutions. Since we solved for \(x\) and found a specific solution, the equation has **one solution**.

Thus, the correct response is:
**The equation has one solution: x equals 0.**