https://file.aiquickdraw.com/mathbot/file/1727305660380gmsffz40.jpg

The inequality in the image is:

\[
15 \geq 3x - 3 > -12
\]

This is a compound inequality, meaning we need to solve for \( x \) such that both inequalities hold true at the same time.

### Step 1: Solve the left part \( 15 \geq 3x - 3 \)
\[
15 \geq 3x - 3
\]
Add 3 to both sides:
\[
18 \geq 3x
\]
Divide by 3:
\[
6 \geq x \quad \text{or} \quad x \leq 6
\]

### Step 2: Solve the right part \( 3x - 3 > -12 \)
\[
3x - 3 > -12
\]
Add 3 to both sides:
\[
3x > -9
\]
Divide by 3:
\[
x > -3
\]

### Step 3: Combine the results
Now we combine the two results:
\[
-3 < x \leq 6
\]

This is the solution to the compound inequality.

Let me know if you'd like more details or have any questions. Here are some related questions to further your understanding:

1. What is the difference between a compound inequality and a regular inequality?
2. How do you check if a solution satisfies both parts of a compound inequality?
3. What happens if one part of a compound inequality is false?
4. How can you graph the solution \( -3 < x \leq 6 \) on a number line?
5. How do inequalities change when you multiply or divide by a negative number?

**Tip:** When solving compound inequalities, always remember to treat each part separately before combining the results!

Learn how to solve the compound inequality 15 ≥ 3x - 3 > -12 with detailed steps. This problem involves solving inequalities and combining the results to find the solution for x. Suitable for students in Grades 7-10.

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