To solve the inequality \(|3x - 6| > 3\), we need to break it into two cases based on the definition of absolute values.

### Case 1: \( 3x - 6 > 3 \)
Solve for \(x\):

\[
3x - 6 > 3
\]

Add 6 to both sides:

\[
3x > 9
\]

Now, divide both sides by 3:

\[
x > 3
\]

### Case 2: \( 3x - 6 < -3 \)
Solve for \(x\):

\[
3x - 6 < -3
\]

Add 6 to both sides:

\[
3x < 3
\]

Now, divide both sides by 3:

\[
x < 1
\]

### Final solution:
The solution to \(|3x - 6| > 3\) is:

\[
x < 1 \quad \text{or} \quad x > 3
\]

In interval notation, the solution is:

\[
(-\infty, 1) \cup (3, \infty)
\]

Would you like more details or have any questions about this?

Here are 5 related questions:
1. What is the solution to \(|2x + 5| > 7\)?
2. How would the solution change if the inequality was \(|3x - 6| \geq 3\)?
3. What is the general approach for solving absolute value inequalities?
4. How do you solve \(|4x - 1| \leq 9\)?
5. How would you graph the solution to \(|3x - 6| > 3\)?

**Tip**: When solving absolute value inequalities, remember that they split into two separate cases—one positive and one negative!

Discover how to solve the absolute value inequality |3x - 6| > 3 through a clear step-by-step solution. This problem explains how to break the inequality into two cases and solve for x. Suitable for students in Grades 8-10, covering key concepts in algebra and inequalities.

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