Solve : `||x| -3| gt 1.`

Explanation

To solve the inequality \( ||x| - 3| > 1 \), we can break it down step by step.

### Step 1: Understand the Absolute Value Inequality
The expression \( ||x| - 3| > 1 \) means that the quantity \( |x| - 3 \) is either greater than 1 or less than -1. Therefore, we can split this into two cases:
1. \( |x| - 3 > 1 \)
2. \( |x| - 3 < -1 \)

### Step 2: Solve the First Case
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