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**Solve 1 ≤ |x - 2| ≤ 3**

**Solution:** We know that:

a ≤ |x - c| ≤ b.

<=> x ∈ [-b + c, -a + c] U [a + c, b + c]

Therefore, 1 ≤ |x - 2| ≤ 3 <=> x ∈ [-3 + 2, -1 + 2] U [1 + 2, 3 + 2]

<=> x ∈ [-1, 1] U [3, 5]

Hence, the solution set of the given inequation is [-1, 1] U [3, 5]