Solve `1 le |x-2| le 3`

Explanation

To solve the inequality \(1 \leq |x - 2| \leq 3\), we will break it down into two parts based on the definition of absolute value.

### Step 1: Break down the absolute value inequality
The inequality \(1 \leq |x - 2| \leq 3\) can be split into two separate inequalities:
1. \( |x - 2| \geq 1 \)
2. \( |x - 2| \leq 3 \)

### Step 2: Solve \( |x - 2| \geq 1 \)
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