The solution set of the inequality $∣ ∣ [| x | - 5] ∣ ∣ - 7 < 0$ is
$([.]$ denotes the greatest integer function $)$

[- 13, 13]

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(- 13, 13)

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(- 13, 13) - {5}

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(- 13, 13) - {\pm 5}

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Solution

The correct option is B $(- 13, 13)$
$∣ ∣ [| x | - 5] ∣ ∣ - 7 < 0$
$\Rightarrow | [| x | - 5] | < 7$
$\Rightarrow - 7 \leq [| x | - 5] \leq 7 \Rightarrow - 7 \leq | x | - 5 < 8 \Rightarrow - 2 \leq | x | < 13 \Rightarrow 0 \leq | x | < 13 \Rightarrow | x | < 13 \Rightarrow x \in (- 13, 13)$

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