https://file.aiquickdraw.com/mathbot/file/1729560155035joi3qsic.jpg

The given inequality to solve is:

\[
-3 |x| > -6
\]

### Step 1: Divide both sides by \(-3\) to eliminate the negative coefficient.

Dividing by a negative number reverses the inequality sign:

\[
|x| < 2
\]

### Step 2: Interpret the absolute value inequality.

The inequality \( |x| < 2 \) means that \(x\) lies between \(-2\) and \(2\). In other words, the solution is:

\[
-2 < x < 2
\]

### Final Answer:
The correct solution is the interval:

\[
(-2, 2)
\]

This matches the first option in the choices provided.

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Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you solve inequalities involving absolute values?
2. What happens when dividing both sides of an inequality by a negative number?
3. Can you explain how to graph the solution \( (-2, 2) \) on a number line?
4. How would the solution change if the inequality was \( |x| \geq 2 \)?
5. What if the original inequality had a different coefficient for \( |x| \)?

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

Learn how to solve the absolute value inequality -3|x| > -6. This problem demonstrates key algebraic techniques, including handling absolute value inequalities and the rule for reversing the inequality when dividing by a negative number. Suitable for students in Grades 9-10.

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