1. **State the problem:** Solve the equation $$\frac{2R_T - 1}{3} = \frac{3R_T + 1}{6}$$ for $R_T$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the least common denominator (LCD) to eliminate fractions. 3. **Find the LCD:** The denominators are 3 and 6, so the LCD is 6. 4. **Multiply both sides by 6:** $$6 \times \frac{2R_T - 1}{3} = 6 \times \frac{3R_T + 1}{6}$$ 5. **Simplify each side:** $$\cancel{6} \times \frac{2R_T - 1}{\cancel{3}} \times 2 = \cancel{6} \times \frac{3R_T + 1}{\cancel{6}}$$ which simplifies to $$2(2R_T - 1) = 3R_T + 1$$ 6. **Expand the left side:** $$4R_T - 2 = 3R_T + 1$$ 7. **Isolate $R_T$ terms:** $$4R_T - 3R_T = 1 + 2$$ 8. **Simplify:** $$R_T = 3$$ **Final answer:** $$R_T = 3$$