We have 1 ≤ |x – 2| ≤ 3
⇒ |x −2| ≥1 and |x −2| ≤3
⇒ (x – 2 ≤ – 1 or x – 2 ≥ 1) and (– 3 ≤ x – 2 ≤ 3)
⇒ (x ≤ 1 or x ≥ 3) and (– 1 ≤ x ≤ 5)
⇒ x ∈ (– ∞, 1] ∪ [3, ∞) and x ∈ [ –1, 5]
Combining the solutions of two inequalities, we have
x ∈ [–1, 1] ∪ [3, 5]
