We are given the compound inequality:

\[
-9 \geq -3x - 3 > -24
\]

We will solve this inequality step by step.

### Step 1: Break the compound inequality into two parts:
1. \(-9 \geq -3x - 3\)
2. \(-3x - 3 > -24\)

#### Solve Part 1: \(-9 \geq -3x - 3\)
1. Add 3 to both sides:
   \[
   -9 + 3 \geq -3x
   \]
   \[
   -6 \geq -3x
   \]

2. Divide by \(-3\) (remember to flip the inequality when dividing by a negative number):
   \[
   \frac{-6}{-3} \leq x
   \]
   \[
   2 \leq x
   \]
   This gives: \(x \geq 2\).

#### Solve Part 2: \(-3x - 3 > -24\)
1. Add 3 to both sides:
   \[
   -3x > -21
   \]

2. Divide by \(-3\) (again, flip the inequality when dividing by a negative number):
   \[
   x < 7
   \]

### Step 2: Combine the results
From the two parts, we have:
\[
x \geq 2 \quad \text{and} \quad x < 7
\]

Thus, the solution is:
\[
2 \leq x < 7
\]

This is the solution to the compound inequality.

---

Would you like further details or have any questions? Here are some related questions you might explore:

1. How do you solve inequalities with fractions?
2. What are the rules for flipping inequality signs?
3. How do you graph the solution to this inequality on a number line?
4. Can a compound inequality have no solution?
5. How does solving absolute value inequalities differ?

**Tip:** When dividing or multiplying by a negative number in inequalities, always remember to flip the inequality sign!

Step-by-step solution for solving the compound inequality −9 ≥ −3x − 3 > −24. Learn the rules of solving inequalities, including adding and dividing with negative numbers, and flipping inequality signs. Suitable for Grades 8-10.

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