We are given the inequality:

\[
-13 \leq -x - 7 \quad \text{or} \quad -16 \geq -x - 7
\]

### Solve the first inequality:
\[
-13 \leq -x - 7
\]

1. Add 7 to both sides:
\[
-13 + 7 \leq -x
\]
\[
-6 \leq -x
\]

2. Multiply both sides by \(-1\) (which reverses the inequality):
\[
6 \geq x
\]

So, from the first inequality, we get:
\[
x \leq 6
\]

### Solve the second inequality:
\[
-16 \geq -x - 7
\]

1. Add 7 to both sides:
\[
-16 + 7 \geq -x
\]
\[
-9 \geq -x
\]

2. Multiply both sides by \(-1\) (again, reversing the inequality):
\[
9 \leq x
\]

So, from the second inequality, we get:
\[
x \geq 9
\]

### Final solution:

The solution to this compound inequality is:
\[
x \leq 6 \quad \text{or} \quad x \geq 9
\]
This means that \( x \) can be any value less than or equal to 6, or any value greater than or equal to 9.

Let me know if you want any more details or have questions!

Here are 5 related questions:
1. What is the difference between "and" and "or" in compound inequalities?
2. How do you graph the solution to this inequality on a number line?
3. What happens if both inequalities are connected by "and" instead of "or"?
4. How do you solve compound inequalities with fractions?
5. What is the process for solving an inequality that contains an absolute value?

**Tip:** Always remember that multiplying or dividing by a negative number reverses the inequality sign.

−13 ≤ −x − 7 or −16 ≥ −x − 7

Learn how to solve the compound inequalities −13 ≤ −x − 7 or −16 ≥ −x − 7. This step-by-step solution explains how to add, subtract, and reverse inequalities when multiplying by negative numbers. Ideal for students in Grades 7-9.

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