1. **State the problem:** Solve for $x$ in the equation $$x - \frac{4}{5} = \frac{1}{2}$$ 2. **Formula and rules:** To isolate $x$, add $\frac{4}{5}$ to both sides of the equation. 3. **Add $\frac{4}{5}$ to both sides:** $$x - \frac{4}{5} + \frac{4}{5} = \frac{1}{2} + \frac{4}{5}$$ which simplifies to $$x = \frac{1}{2} + \frac{4}{5}$$ 4. **Find common denominator:** The denominators are 2 and 5. The least common denominator is 10. Convert each fraction: $$\frac{1}{2} = \frac{5}{10}, \quad \frac{4}{5} = \frac{8}{10}$$ 5. **Add the fractions:** $$x = \frac{5}{10} + \frac{8}{10} = \frac{13}{10}$$ 6. **Final answer:** $$x = \frac{13}{10}$$ or as a decimal, $$x = 1.3$$