Solve `0 lt |x| lt 2`

Explanation

To solve the inequality \(0 < |x| < 2\), we will break it down into two parts: \( |x| > 0 \) and \( |x| < 2 \).

### Step 1: Solve \( |x| > 0 \)

The absolute value \( |x| \) is defined as the distance of \( x \) from 0 on the number line. Therefore, \( |x| > 0 \) means that \( x \) cannot be equal to 0. This gives us:

\[
x \in \mathbb{R} \setminus \{0\}
...