1. **State the problem:** Solve the compound inequality $-4a < 20$ and $-9 > a - 6$. 2. **Solve the first inequality:** $$-4a < 20$$ Divide both sides by $-4$, remembering to reverse the inequality sign because we divide by a negative number: $$\cancel{-4}a > \frac{20}{\cancel{-4}}$$ $$a > -5$$ 3. **Solve the second inequality:** $$-9 > a - 6$$ Add 6 to both sides: $$-9 + 6 > a - 6 + 6$$ $$-3 > a$$ This can be rewritten as: $$a < -3$$ 4. **Combine the inequalities:** We have: $$a > -5$$ $$a < -3$$ So the solution is: $$-5 < a < -3$$ 5. **Explanation:** The solution set includes all values of $a$ strictly between $-5$ and $-3$. Final answer: $$-5 < a < -3$$