Let's solve the equation \( 5(2x+2) - 4 = 2x + 6 \).
First, simplify the left side:
\[ 5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6 \]
So now the equation is:
\[ 10x + 6 = 2x + 6 \]
Next, we can subtract \( 2x \) from both sides:
\[ 10x - 2x + 6 = 6 \]
This simplifies to:
\[ 8x + 6 = 6 \]
Now, subtract 6 from both sides:
\[ 8x = 0 \]
Now, divide by 8:
\[ x = 0 \]
Lastly, let's check if there are infinite solutions or one solution. We can see that \( 10x + 6 = 2x + 6 \) is true for only the particular value of \( x = 0 \), and both sides of the equation reduce to \( 6 \).
Thus, the equation has one solution: \( x = 0 \).
The correct responses are:
- The equation has one solution: \( x = 0 \).