Question

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

• A. $10$
• B. $13$
• C. $18$
• D. $28$

Answer 1

The correct option is B $13$

$||x-1|-2|<5\Rightarrow -5<|x-1|-2<5\Rightarrow -3<|x-1|<7\Rightarrow 0\le |x-1|<7\Rightarrow -7<x-1<7\Rightarrow -6<x<8$
Hence, number of integral values is $13$