1. **State the problem:** Solve the equation $2x - \frac{4}{5} = 2$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse operations. 3. **Step 1:** Add $\frac{4}{5}$ to both sides to eliminate the fraction on the left: $$2x - \frac{4}{5} + \frac{4}{5} = 2 + \frac{4}{5}$$ which simplifies to $$2x = 2 + \frac{4}{5}$$ 4. **Step 2:** Convert 2 to a fraction with denominator 5 to add easily: $$2 = \frac{10}{5}$$ so $$2x = \frac{10}{5} + \frac{4}{5} = \frac{14}{5}$$ 5. **Step 3:** Divide both sides by 2 to solve for $x$: $$x = \frac{\frac{14}{5}}{2} = \frac{14}{5} \times \frac{1}{2} = \frac{14}{10} = \frac{7}{5}$$ 6. **Final answer:** $$x = \frac{7}{5}$$ This means $x$ equals seven fifths or 1.4 in decimal form.