Let's carefully go through the problem and verify the solution step by step.
We are given the inequality:
$$
2|3x + 9| < 36
$$
---
Step 1: Divide both sides by 2
$$
\frac{2|3x + 9|}{2} < \frac{36}{2}
$$
$$
|3x + 9| < 18
$$
This is correct.
---
Step 2: Use the definition of absolute value inequality
For $ |A| < B $, where $ B > 0 $, we have:
$$
-B < A < B
$$
So:
$$
-18 < 3x + 9 < 18
$$
Correct so far.
---
Step 3: Subtract 9 from all parts
$$
-18 - 9 < 3x + 9 - 9 < 18 - 9
$$
$$
-27 < 3x < 9
$$
Still correct.
---
Step 4: Divide all parts by 3
$$
\frac{-27}{3} < \frac{3x}{3} < \frac{9}{3}
$$
$$
-9 < x < 3
$$
✔ This is the final solution.
---
✔ Final Answer:
$$
\boxed{-9 < x < 3}
$$
---
📌 Explanation:
The original inequality involves an absolute value. We solved it by:
1. Isolating the absolute value expression.
2. Converting the absolute value inequality into a compound inequality.
3. Solving for $ x $ by performing the same operations on all three parts.
This gives us the set of all real numbers $ x $ such that $ x $ is greater than $-9$ and less than $3$.
---
✔ The steps in your image are
correct, and the final answer is:
$$
\boxed{-9 < x < 3}
$$
Parent Tip: Review the logic above to help your child master the concept of inequalities involving absolute value worksheet.
