Question
The number of integers satisfying the inequality ∣∣|x−1|−2∣∣<5, is
The number of integers satisfying the inequality ∣∣|x−1|−2∣∣<5, is
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Solution
The correct option is B 13
∣∣|x−1|−2∣∣<5⇒−5<|x−1|−2<5⇒−3<|x−1|<7⇒0≤|x−1|<7⇒−7<x−1<7⇒−6<x<8
Hence, number of integral values is 13
∣∣|x−1|−2∣∣<5⇒−5<|x−1|−2<5⇒−3<|x−1|<7⇒0≤|x−1|<7⇒−7<x−1<7⇒−6<x<8
Hence, number of integral values is 13
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