1. **State the problem:** Solve the equation $$\frac{2x}{3} - \frac{1}{2} = \frac{1}{4}$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation. 3. **Add $\frac{1}{2}$ to both sides:** $$\frac{2x}{3} - \frac{1}{2} + \frac{1}{2} = \frac{1}{4} + \frac{1}{2}$$ which simplifies to $$\frac{2x}{3} = \frac{1}{4} + \frac{1}{2}$$ 4. **Find a common denominator to add the fractions on the right:** $$\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$ 5. **Rewrite the equation:** $$\frac{2x}{3} = \frac{3}{4}$$ 6. **Multiply both sides by 3 to clear the denominator on the left:** $$3 \times \frac{2x}{3} = 3 \times \frac{3}{4}$$ $$\cancel{3} \times \frac{2x}{\cancel{3}} = \frac{9}{4}$$ which simplifies to $$2x = \frac{9}{4}$$ 7. **Divide both sides by 2 to solve for $x$:** $$x = \frac{\frac{9}{4}}{2} = \frac{9}{4} \times \frac{1}{2} = \frac{9}{8}$$ **Final answer:** $$x = \frac{9}{8}$$