1. **State the problem:** Solve the inequality $8 < 2 - 2(3x - 1) + \frac{4}{5}x$. 2. **Apply distributive property:** Expand $-2(3x - 1)$ to get $-6x + 2$. 3. **Rewrite the inequality:** $$8 < 2 - 6x + 2 + \frac{4}{5}x$$ 4. **Combine like terms on the right side:** $$8 < 4 - 6x + \frac{4}{5}x$$ 5. **Isolate variable terms:** Subtract 4 from both sides: $$8 - 4 < -6x + \frac{4}{5}x$$ $$4 < -6x + \frac{4}{5}x$$ 6. **Combine the $x$ terms:** $$-6x + \frac{4}{5}x = -\frac{30}{5}x + \frac{4}{5}x = -\frac{26}{5}x$$ So the inequality is: $$4 < -\frac{26}{5}x$$ 7. **Solve for $x$:** Divide both sides by $-\frac{26}{5}$, remembering to reverse the inequality sign because dividing by a negative number flips the inequality: $$x < \frac{4}{-\frac{26}{5}}$$ $$x < 4 \times -\frac{5}{26}$$ $$x < -\frac{20}{26}$$ 8. **Simplify the fraction:** $$x < -\frac{10}{13}$$ **Final answer:** $$x < -\frac{10}{13}$$