1. **State the problem:** Solve the equation $$-\frac{1}{2}(y - 3) = \frac{25}{4}$$ for $y$. 2. **Write down the formula and rules:** To solve for $y$, we need to isolate $y$ on one side of the equation. This involves multiplying or dividing both sides by numbers and simplifying. 3. **Multiply both sides by $-2$ to cancel the fraction on the left:** $$-2 \times \left(-\frac{1}{2}(y - 3)\right) = -2 \times \frac{25}{4}$$ 4. **Simplify both sides:** $$\cancel{-2} \times \left(-\frac{1}{\cancel{2}}(y - 3)\right) = -\frac{50}{4}$$ $$y - 3 = -\frac{50}{4}$$ 5. **Simplify the fraction on the right:** $$y - 3 = -\frac{25}{2}$$ 6. **Add 3 to both sides to isolate $y$:** $$y - 3 + 3 = -\frac{25}{2} + 3$$ 7. **Simplify the right side by converting 3 to a fraction with denominator 2:** $$y = -\frac{25}{2} + \frac{6}{2}$$ 8. **Add the fractions:** $$y = -\frac{25}{2} + \frac{6}{2} = -\frac{19}{2}$$ **Final answer:** $$y = -\frac{19}{2}$$