Question

The set of real values of $x$ satisfying $||x-1|-1|\le 2,$ is

• A. $[2,4]$
• B. $[-2,4]$
• C. $[-4,-2]$
• D. $[-1,\infty )$

Answer 1

The correct option is B $[-2,4]$

$||x-1|-1|\le 2$
$\Rightarrow -2\le |x-1|-1\le 2$
$\Rightarrow -1\le |x-1|\le 3$
$\Rightarrow 0\le |x-1|\le 3(\because |x-1|\ge 0\forall x\in R)$
$\Rightarrow -3\le x-1\le 3$
$\Rightarrow -2\le x\le 4$