The number of integers satisfying the inequality $∣ ∣ | x - 1 | - 2 ∣ ∣ < 5,$ is

10

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13

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18

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28

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Solution

The correct option is B $13$
$∣ ∣ | x - 1 | - 2 ∣ ∣ < 5 \Rightarrow - 5 < | x - 1 | - 2 < 5 \Rightarrow - 3 < | x - 1 | < 7 \Rightarrow 0 \leq | x - 1 | < 7 \Rightarrow - 7 < x - 1 < 7 \Rightarrow - 6 < x < 8$
Hence, number of integral values is $13$

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