1. **State the problem:** Solve the equation $3x + 2 = \frac{2x + 13}{3}$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the denominator to clear the fraction. 3. **Multiply both sides by 3:** $$3(3x + 2) = 3 \times \frac{2x + 13}{3}$$ which simplifies to $$9x + 6 = 2x + 13$$ 4. **Isolate variable terms:** Subtract $2x$ from both sides: $$9x - 2x + 6 = 13$$ $$7x + 6 = 13$$ 5. **Isolate $x$:** Subtract 6 from both sides: $$7x = 13 - 6$$ $$7x = 7$$ 6. **Solve for $x$:** Divide both sides by 7: $$x = \frac{7}{7} = 1$$ **Final answer:** $x = 1$