To solve for \( b \) in the equation
\[ A = \frac{1}{2} (a + b), \]
follow these steps:
- Multiply both sides by 2 to eliminate the fraction:
\[ 2A = a + b. \]
- Rearrange the equation to isolate \( b \):
\[ b = 2A - a. \]
Thus, the solution for \( b \) is
\[ b = 2A - a. \]