1. **State the problem:** Solve the equation $$\frac{x}{3} + 4 = \frac{5}{2}$$ for $x$. 2. **Isolate the variable term:** Subtract 4 from both sides to get $$\frac{x}{3} = \frac{5}{2} - 4$$. 3. **Simplify the right side:** Convert 4 to a fraction with denominator 2: $$4 = \frac{8}{2}$$, so $$\frac{5}{2} - \frac{8}{2} = \frac{5 - 8}{2} = \frac{-3}{2}$$. 4. **Rewrite the equation:** $$\frac{x}{3} = \frac{-3}{2}$$. 5. **Solve for $x$ by multiplying both sides by 3:** $$x = 3 \times \frac{-3}{2}$$ 6. **Calculate the product:** $$x = \frac{3 \times -3}{2} = \frac{-9}{2}$$. **Final answer:** $$x = \frac{-9}{2}$$.