1. **State the problem:** Solve the compound inequality $$k - 10 \leq -5 \text{ or } k - 11 \geq -4$$ for $k$. 2. **Solve the first inequality:** $$k - 10 \leq -5$$ Add 10 to both sides: $$k - 10 + 10 \leq -5 + 10$$ $$k \leq 5$$ 3. **Solve the second inequality:** $$k - 11 \geq -4$$ Add 11 to both sides: $$k - 11 + 11 \geq -4 + 11$$ $$k \geq 7$$ 4. **Write the solution as a compound inequality:** $$k \leq 5 \text{ or } k \geq 7$$ 5. **Explanation:** The solution means $k$ can be any number less than or equal to 5, or any number greater than or equal to 7. Values between 5 and 7 are not included. **Final answer:** $$k \leq 5 \text{ or } k \geq 7$$