Question

On a number line, show all the points that represent the following values of x.
|×| >2

Answer 1

To solve the inequality \(|x| > 2\), we need to interpret what this means on a number line.

The absolute value inequality \(|x| > 2\) implies two conditions:

1. \(x > 2\)
2. \(x < -2\)

This means that \(x\) can be any value that is either greater than \(2\) or less than \(-2\).

### Steps to represent on a number line:

1. Mark the points \(2\) and \(-2\) on the number line.
2. Since the inequality is strict (greater than, not greater than or equal to), we will use an open circle at the points \(2\) and \(-2\) to indicate that these points are not included in the solution.
3. Shade the region to the right of \(2\) (this represents \(x > 2\)).
4. Shade the region to the left of \(-2\) (this represents \(x < -2\)).

### Visual Representation:

```
<---|---|---|---|---|---|---|---|---|--->
-3 -2 -1 0 1 2 3

o---------------> (x > 2)
<--------------o (x < -2)
```

In this representation:
- The open circles at \(-2\) and \(2\) indicate that those values are not included in the solution.
- The arrows extending to the right and left indicate that all values in those regions satisfy the inequality \(|x| > 2\).