The correct option is B (−∞,−12]∪[12,32]∪[52,∞)
|(2|x−1|−2)|≥1⇒|(|x−1|−1)|≥12
Let |x−1|−1=t⇒|t|≥12
⇒t≤−12 or t≥12
⇒|x−1|−1≤−12 or |x−1|−1≥12
⇒|x−1|≤12 or |x−1|≥32
⇒(x−1)∈[−12,12] or (x−1)∈(−∞,−32]∪[32,∞)
⇒x∈[12,32] or x∈(−∞,−12]∪[52,∞)
∴x∈(−∞,−12]∪[12,32]∪[52,∞)