1. State the problem: Solve the equation $$\frac{r}{2} = \frac{1}{2} + \frac{2r}{5}$$ for $r$. 2. Eliminate the denominators by multiplying both sides of the equation by the least common denominator, which is 10: $$10 \times \frac{r}{2} = 10 \times \frac{1}{2} + 10 \times \frac{2r}{5}$$ This simplifies to: $$5r = 5 + 4r$$ 3. Isolate $r$ by subtracting $4r$ from both sides: $$5r - 4r = 5$$ which simplifies to: $$r = 5$$ 4. Final answer: The solution to the equation is $$r = 5$$.