1. **State the problem:** Solve the compound inequality $$x \leq -4 \text{ or } x \geq 10$$ and represent the solution on a number line and in interval notation. 2. **Understand the inequality:** The word "or" means the solution includes all values that satisfy either $$x \leq -4$$ or $$x \geq 10$$. 3. **Write the solution set:** - For $$x \leq -4$$, the solution includes all numbers less than or equal to $$-4$$. - For $$x \geq 10$$, the solution includes all numbers greater than or equal to $$10$$. 4. **Interval notation:** $$(-\infty, -4] \cup [10, \infty)$$ 5. **Graph interpretation:** - The graph should show a solid line and arrow pointing left starting at $$-4$$ (including $$-4$$). - Also, a solid line and arrow pointing right starting at $$10$$ (including $$10$$). 6. **Choose the correct graph:** Option C matches this description. **Final answer:** The solution set is $$(-\infty, -4] \cup [10, \infty)$$ and the correct graph is Option C.