1. **State the problem:** Solve the equation $$\frac{x}{4} + \frac{3}{2} = 5$$ for $x$. 2. **Identify the formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. This involves subtracting and multiplying both sides appropriately. 3. **Subtract $\frac{3}{2}$ from both sides:** $$\frac{x}{4} + \frac{3}{2} - \frac{3}{2} = 5 - \frac{3}{2}$$ $$\frac{x}{4} = 5 - \frac{3}{2}$$ 4. **Calculate the right side:** Convert 5 to a fraction with denominator 2: $$5 = \frac{10}{2}$$ So, $$\frac{x}{4} = \frac{10}{2} - \frac{3}{2} = \frac{10 - 3}{2} = \frac{7}{2}$$ 5. **Multiply both sides by 4 to solve for $x$:** $$4 \times \frac{x}{4} = 4 \times \frac{7}{2}$$ $$\cancel{4} \times \frac{x}{\cancel{4}} = \frac{4 \times 7}{2}$$ $$x = \frac{28}{2}$$ 6. **Simplify the fraction:** $$x = 14$$ **Final answer:** $$x = 14$$