1. The problem involves solving the equation $1 - \frac{1}{2} = 2a$ for $a$. 2. First, simplify the left side: $$1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}$$ 3. So the equation becomes: $$\frac{1}{2} = 2a$$ 4. To solve for $a$, divide both sides by 2: $$a = \frac{\frac{1}{2}}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$$ 5. Therefore, the solution is: $$a = \frac{1}{4}$$ This means that when $a$ is $\frac{1}{4}$, the original equation holds true.