To solve the equation \( 5(2x + 2) - 4 = 2x + 6 \), we will first simplify both sides.
- Distribute \( 5 \) on the left side:
\[ 5(2x + 2) = 10x + 10 \]
So the equation becomes:
\[ 10x + 10 - 4 = 2x + 6 \]
- Combine like terms on the left side:
\[ 10x + 6 = 2x + 6 \]
- Now, isolate the \( x \) terms by subtracting \( 2x \) from both sides:
\[ 10x - 2x + 6 = 6 \]
This simplifies to:
\[ 8x + 6 = 6 \]
- Subtract \( 6 \) from both sides:
\[ 8x = 0 \]
- Finally, divide by \( 8 \):
\[ x = 0 \]
Now, we determine how many solutions the equation has. We found a single solution, \( x = 0 \).
Thus, the answer is: The equation has one solution: \( x = 0 \).