1. The problem is to simplify the expression $-7 \pm \sqrt{\frac{1}{4}}$. 2. Start by simplifying the square root: $\sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}} = \frac{1}{2}$. 3. Substitute back into the expression, giving two cases: - Case 1: $-7 + \frac{1}{2} = -\frac{14}{2} + \frac{1}{2} = -\frac{13}{2}$. - Case 2: $-7 - \frac{1}{2} = -\frac{14}{2} - \frac{1}{2} = -\frac{15}{2}$. 4. Therefore, the simplified answers are $-\frac{13}{2}$ and $-\frac{15}{2}$.