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The inequality provided is \( |x| > 2 \). To solve and graph this inequality, we need to understand what the absolute value inequality means:

1. \( |x| > 2 \) implies that the distance of \(x\) from 0 is greater than 2. In other words, \(x\) is either less than -2 or greater than 2.
   
   - This splits into two inequalities: 
     \[
     x < -2 \quad \text{or} \quad x > 2
     \]

In terms of a number line:

- The solution consists of two regions: one to the left of -2 and one to the right of 2.
- The values at \(x = -2\) and \(x = 2\) are not included in the solution, so we use open circles at -2 and 2.
- The graph should have arrows extending leftward from -2 and rightward from 2, representing all values less than -2 and greater than 2.

### Correct Answer:
The correct graph will have open circles at -2 and 2, with shaded lines extending outwards from these points (to the left of -2 and to the right of 2).

From the image:
- The bottom-right graph correctly represents the inequality \( |x| > 2 \), with open circles at -2 and 2 and shading to the left of -2 and right of 2.

Would you like more details or have any questions?

Here are five related questions to expand on this concept:

1. How would you graph \( |x| \geq 2 \) instead of \( |x| > 2 \)?
2. What does the graph of \( |x| < 2 \) look like?
3. How do you solve inequalities with absolute values inside a quadratic equation?
4. How do you represent compound inequalities on a number line?
5. What real-life scenarios can be modeled by absolute value inequalities?

**Tip:** When graphing absolute value inequalities, always remember to split the inequality into two cases and check whether to include or exclude the boundary points (using open or closed circles).

Learn how to graph the absolute value inequality |x| > 2 on a number line. This involves key algebraic concepts such as solving inequalities with absolute values and graphing them correctly. Suitable for students in Grades 8-10.

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