Let's solve the equation step by step to determine how many solutions it has.
The given equation is:
\[ 5(2x + 2) - 4 = 2x + 6 \]
First, distribute the 5 on the left side:
\[ 10x + 10 - 4 = 2x + 6 \]
Now, simplify the left side:
\[ 10x + 6 = 2x + 6 \]
Next, we will move the \(2x\) from the right side to the left side by subtracting \(2x\) from both sides:
\[ 10x - 2x + 6 = 6 \]
This simplifies to:
\[ 8x + 6 = 6 \]
Now, subtract 6 from both sides:
\[ 8x = 0 \]
Finally, divide both sides by 8:
\[ x = 0 \]
Now, we find that we have one solution:
The equation has one solution: x equals 0.