To solve the inequality \(-x - 8 \geq -5\), follow these steps:

1. **Add 8 to both sides**:
   \[
   -x \geq -5 + 8
   \]
   \[
   -x \geq 3
   \]

2. **Multiply both sides by \(-1\)**, and remember to **reverse the inequality** sign when multiplying by a negative number:
   \[
   x \leq -3
   \]

So, the solution is:
\[
x \leq -3
\]

### Final Answer: \( x \leq -3 \)

Would you like further details on solving inequalities, or do you have any questions?

Here are five related questions to deepen your understanding:
1. How do you solve inequalities involving variables on both sides?
2. What happens when you multiply or divide an inequality by a negative number?
3. Can you explain how to graph the solution \(x \leq -3\) on a number line?
4. How do you solve compound inequalities (like \(a < x \leq b\))?
5. What are the key differences between solving equations and inequalities?

**Tip**: Always reverse the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the inequality x - 8 ≥ -5 with a detailed step-by-step explanation. This problem covers important algebraic concepts such as inequalities, sign reversal when multiplying by a negative number, and is suitable for students in Grades 6-8.

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