1. **State the problem:** Solve the equation $$-\frac{1}{2}(y - 3) = \frac{25}{4}$$ for $y$. 2. **Use the distributive property:** Multiply both sides by $-2$ to eliminate the fraction and the negative sign. $$-\frac{1}{2}(y - 3) = \frac{25}{4}$$ Multiply both sides by $-2$: $$\cancel{-2} \times -\frac{1}{2}(y - 3) = \cancel{-2} \times \frac{25}{4}$$ This simplifies to: $$(y - 3) = -\frac{50}{4}$$ 3. **Simplify the right side:** $$-\frac{50}{4} = -\frac{25}{2}$$ 4. **Isolate $y$:** Add 3 to both sides: $$y - 3 + 3 = -\frac{25}{2} + 3$$ $$y = -\frac{25}{2} + \frac{6}{2}$$ 5. **Combine the fractions:** $$y = -\frac{25}{2} + \frac{6}{2} = -\frac{19}{2}$$ **Final answer:** $$y = -\frac{19}{2}$$