Question

Solve for a to determine if the equation has one, none, or infinite solutions.

5(2x + 2) - 4 = 2x + 6 (1 point)

The equation has one solution: x = 1

The equation has infinite solutions.

The equation has one solution: x = 0

The equation has no solution.

Answer 1

To solve the equation \(5(2x + 2) - 4 = 2x + 6\), we start by simplifying both sides.

1. Distributive property:
\[
5(2x + 2) = 10x + 10
\]

Substitute this back into the equation:
\[
10x + 10 - 4 = 2x + 6
\]

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

3. Now, we can isolate \(x\) by subtracting \(2x\) from both sides:
\[
10x - 2x + 6 = 6
\]
\[
8x + 6 = 6
\]

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

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

Now, we need to check how many solutions this equation has:

- We have found \(x = 0\), and the steps followed show a consistent relationship demonstrated in the equation.

This tells us that the equation has **one solution: \(x = 0\)**.

Thus, the correct answer is:
**The equation has one solution: x = 0.**