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

To solve the equation \( 5(2x + 2) - 4 = 2x + 6 \), let's start by simplifying both sides:

1. Distribute the 5 on the left side:

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

   So, the equation now looks like this:

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

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

   \[ 10x - 2x + 6 = 6 \] \[ 8x + 6 = 6 \]

3. Now, subtract 6 from both sides:

   \[ 8x + 6 - 6 = 6 - 6 \] \[ 8x = 0 \]

4. Finally, divide both sides by 8:

   \[ x = \frac{0}{8} = 0 \]

Now we can analyze the solution.

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

Thus, the correct response is:

• The equation has one solution: \( x = 0 \).