Question: Solve the compound inequality.
x + 8 < 0 or 3x > -21
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. The solution is x < □.
B. The solution is x > □.
C. The solution is □ < x < □.
D. The solution is x > □ or x < □.
E. The solution is all real numbers.
F. There is no solution.
1. **State the problem:** Solve the compound inequality $$x + 8 < 0 \text{ or } 3x > -21$$.
2. **Solve each inequality separately:**
- For $$x + 8 < 0$$:
$$x < -8$$
- For $$3x > -21$$:
Divide both sides by 3:
$$\cancel{3}x > \frac{-21}{\cancel{3}}$$
$$x > -7$$
3. **Combine the solutions:**
Since the compound inequality uses "or", the solution is all $$x$$ such that $$x < -8$$ or $$x > -7$$.
4. **Interpretation:**
This means the solution set includes all numbers less than $$-8$$ and all numbers greater than $$-7$$.
5. **Answer choice:**
The solution is $$x < -8$$ or $$x > -7$$, which corresponds to choice D.
**Final answer:** $$x < -8 \text{ or } x > -7$$.