Let's solve the equation step by step:
The equation is:
\[ 3(2x + 2) - 4 = -2x + 10 \]
- Distribute on the left side:
\[ 6x + 6 - 4 = -2x + 10 \]
- Combine like terms on the left side:
\[ 6x + 2 = -2x + 10 \]
- Add \( 2x \) to both sides to get all \( x \) terms on one side:
\[ 6x + 2x + 2 = 10 \]
This simplifies to:
\[ 8x + 2 = 10 \]
- Subtract 2 from both sides:
\[ 8x = 8 \]
- Divide by 8:
\[ x = 1 \]
Now, let's determine the type of solution. Since we found a single value for \( x \) (which is \( x = 1 \)), the equation has one solution.
Thus, the correct response is:
The equation has one solution: x = 1.