1. **State the problem:** Solve the inequality $$\frac{3x - 2 - x}{\frac{4}{5}} \geq -1$$. 2. **Simplify the numerator:** Combine like terms in the numerator: $$3x - 2 - x = (3x - x) - 2 = 2x - 2$$. 3. **Rewrite the inequality:** The expression becomes $$\frac{2x - 2}{\frac{4}{5}} \geq -1$$. 4. **Divide by a fraction:** Dividing by $$\frac{4}{5}$$ is the same as multiplying by its reciprocal $$\frac{5}{4}$$: $$\left(2x - 2\right) \times \frac{5}{4} \geq -1$$. 5. **Write the multiplication explicitly:** $$\frac{5}{4} (2x - 2) \geq -1$$. 6. **Distribute $$\frac{5}{4}$$:** $$\frac{5}{4} \times 2x - \frac{5}{4} \times 2 \geq -1$$ $$= \frac{10}{4}x - \frac{10}{4} \geq -1$$ 7. **Simplify fractions:** $$\frac{10}{4} = \frac{5}{2}$$, so $$\frac{5}{2}x - \frac{5}{2} \geq -1$$. 8. **Add $$\frac{5}{2}$$ to both sides:** $$\frac{5}{2}x - \frac{5}{2} + \frac{5}{2} \geq -1 + \frac{5}{2}$$ $$\Rightarrow \frac{5}{2}x \geq -1 + \frac{5}{2}$$. 9. **Calculate right side:** $$-1 + \frac{5}{2} = -\frac{2}{2} + \frac{5}{2} = \frac{3}{2}$$. 10. **Divide both sides by $$\frac{5}{2}$$:** $$x \geq \frac{\frac{3}{2}}{\frac{5}{2}}$$ 11. **Simplify division:** $$x \geq \frac{3}{2} \times \frac{2}{5} = \frac{3}{5}$$. **Final answer:** $$x \geq \frac{3}{5}$$. This means all values of $$x$$ greater than or equal to $$\frac{3}{5}$$ satisfy the inequality.