1. **State the problem:** Solve the equation $$12 - \frac{1}{5}r = 2r + 1$$ for $r$. 2. **Write down the equation:** $$12 - \frac{1}{5}r = 2r + 1$$ 3. **Goal:** Isolate $r$ on one side. 4. **Subtract 1 from both sides:** $$12 - 1 - \frac{1}{5}r = 2r$$ $$11 - \frac{1}{5}r = 2r$$ 5. **Add $\frac{1}{5}r$ to both sides to get all $r$ terms on the right:** $$11 = 2r + \frac{1}{5}r$$ 6. **Combine like terms on the right:** $$2r + \frac{1}{5}r = \frac{10}{5}r + \frac{1}{5}r = \frac{11}{5}r$$ So, $$11 = \frac{11}{5}r$$ 7. **Multiply both sides by $\frac{5}{11}$ to solve for $r$:** $$r = 11 \times \frac{5}{11} = 5$$ **Final answer:** $$r = 5$$