1. **State the problem:** Solve the equation $$-\frac{1}{2} = -\frac{1}{2}a + \frac{3}{4}$$ for the variable $a$. 2. **Isolate the term with $a$:** Subtract $\frac{3}{4}$ from both sides to get all constants on one side: $$-\frac{1}{2} - \frac{3}{4} = -\frac{1}{2}a$$ 3. **Find a common denominator and simplify the left side:** $$-\frac{1}{2} = -\frac{2}{4}$$ so $$-\frac{2}{4} - \frac{3}{4} = -\frac{5}{4}$$ Thus, $$-\frac{5}{4} = -\frac{1}{2}a$$ 4. **Divide both sides by $-\frac{1}{2}$ to solve for $a$:** $$a = \frac{-\frac{5}{4}}{-\frac{1}{2}}$$ Show cancellation: $$a = \frac{\cancel{-}\frac{5}{4}}{\cancel{-}\frac{1}{2}} = \frac{\frac{5}{4}}{\frac{1}{2}}$$ 5. **Divide the fractions by multiplying by the reciprocal:** $$a = \frac{5}{4} \times \frac{2}{1} = \frac{5 \times 2}{4 \times 1} = \frac{10}{4}$$ 6. **Simplify the fraction:** $$a = \frac{10}{4} = \frac{5}{2}$$ **Final answer:** $$a = \frac{5}{2}$$