We know that,

a≤ | x – c | ≤ b ⟺ x ϵ [–b+c, –a+c] ⋃ [a+c, b+c]

∴, 1≤|x–2|≤3 ⟺ xϵ [–3+2, –1+2] ⋃ [1+2, 3+2]

⟺xϵ [–1, 1]⋃[3, 5]

We can verify the answers using graph as well.