1. **State the problem:** Solve the compound inequality $$x + 9 < 0 \text{ or } 2x > -12$$. 2. **Solve the first inequality:** $$x + 9 < 0$$ Subtract 9 from both sides: $$x + \cancel{9} - 9 < 0 - 9$$ $$x < -9$$ 3. **Solve the second inequality:** $$2x > -12$$ Divide both sides by 2: $$\frac{2x}{\cancel{2}} > \frac{-12}{\cancel{2}}$$ $$x > -6$$ 4. **Combine the solutions:** The compound inequality uses "or", so the solution is all values of $x$ such that: $$x < -9 \text{ or } x > -6$$ 5. **Interpretation:** This means $x$ can be any number less than $-9$ or any number greater than $-6$. Values between $-9$ and $-6$ are not included. **Final answer:** $$x < -9 \text{ or } x > -6$$