Solve `|x|+|x-2|=2.`

Explanation

To solve the equation \( |x| + |x - 2| = 2 \), we need to consider different cases based on the critical points where the expressions inside the absolute values change sign. The critical points here are \( x = 0 \) and \( x = 2 \).

### Step 1: Identify the cases
We will break the problem into three cases based on the critical points:
1. Case 1: \( x < 0 \)
2. Case 2: \( 0 \leq x < 2 \)
3. Case 3: \( x \geq 2 \)

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