1. **State the problem:** Solve the inequality $$\frac{8}{3} u < -12$$ for $u$. 2. **Formula and rules:** To solve inequalities involving multiplication or division by a negative number, remember to reverse the inequality sign. 3. **Isolate $u$:** Divide both sides by $\frac{8}{3}$ to isolate $u$: $$u < \frac{-12}{\frac{8}{3}}$$ 4. **Simplify the division:** Dividing by a fraction is the same as multiplying by its reciprocal: $$u < -12 \times \frac{3}{8}$$ 5. **Calculate the product:** $$u < \frac{-12 \times 3}{8} = \frac{-36}{8}$$ 6. **Simplify the fraction:** $$u < \frac{\cancel{-36}}{\cancel{8}} = \frac{-9}{2}$$ 7. **Final answer:** $$u < -\frac{9}{2}$$ This means $u$ is any number less than $-\frac{9}{2}$.