To solve the equation \(\frac{1}{2}(4x - 4) = x + 3\), follow these steps:
- Distribute \(\frac{1}{2}\) on the left side:
\[ \frac{1}{2}(4x) - \frac{1}{2}(4) = 2x - 2 \]
So, the equation becomes:
\[ 2x - 2 = x + 3 \]
- Isolate \(x\) by subtracting \(x\) from both sides:
\[ 2x - x - 2 = 3 \]
This simplifies to:
\[ x - 2 = 3 \]
- Now, add 2 to both sides:
\[ x = 3 + 2 \]
Thus:
\[ x = 5 \]
The solution is:
\[ \boxed{5} \]