1. **Stating the problem:** Solve the inequality $n + 2 \leq -5$ and $n + 6 \leq -6$ for $n$. 2. **First inequality:** $n + 2 \leq -5$ Subtract 2 from both sides: $$n + 2 - \cancel{2} \leq -5 - \cancel{2}$$ $$n \leq -7$$ 3. **Second inequality:** $n + 6 \leq -6$ Subtract 6 from both sides: $$n + 6 - \cancel{6} \leq -6 - \cancel{6}$$ $$n \leq -12$$ 4. **Combine both inequalities with AND:** Since both must be true, $n$ must satisfy both $n \leq -7$ and $n \leq -12$. The more restrictive condition is $n \leq -12$. **Final solution:** $$n \leq -12$$