1. **State the problem:** Solve the equation $$\frac{1}{2}r - \frac{3}{4} = \frac{1}{2}$$ for $r$. 2. **Isolate the variable term:** Add $\frac{3}{4}$ to both sides to get rid of the constant on the left: $$\frac{1}{2}r = \frac{1}{2} + \frac{3}{4}$$ 3. **Find a common denominator and add the fractions:** $$\frac{1}{2} = \frac{2}{4}$$ so $$\frac{2}{4} + \frac{3}{4} = \frac{5}{4}$$ 4. **Rewrite the equation:** $$\frac{1}{2}r = \frac{5}{4}$$ 5. **Solve for $r$ by multiplying both sides by the reciprocal of $\frac{1}{2}$, which is 2:** $$r = 2 \times \frac{5}{4} = \frac{10}{4}$$ 6. **Simplify the fraction:** $$\frac{10}{4} = \frac{5}{2}$$ **Final answer:** $$r = \frac{5}{2}$$