1. **State the problem:** Solve the inequality $$\frac{x - 1}{3} > 3x - \frac{4}{3}$$. 2. **Write the inequality clearly:** $$\frac{x - 1}{3} > 3x - \frac{4}{3}$$ 3. **Eliminate the denominators by multiplying both sides by 3:** $$3 \times \frac{x - 1}{3} > 3 \times \left(3x - \frac{4}{3}\right)$$ 4. **Simplify both sides:** $$\cancel{3} \times \frac{x - 1}{\cancel{3}} > 9x - 4$$ $$x - 1 > 9x - 4$$ 5. **Bring all terms involving $x$ to one side and constants to the other:** $$x - 9x > -4 + 1$$ $$-8x > -3$$ 6. **Divide both sides by $-8$ to isolate $x$. Remember to reverse the inequality sign when dividing by a negative number:** $$\frac{-8x}{-8} < \frac{-3}{-8}$$ $$x < \frac{3}{8}$$ **Final answer:** $$x < \frac{3}{8}$$