Question

The set of real values of $x$ satisfying $|x-1|\le 3$ and $|x-1|\ge 1$

• A. $[2,4]$
• B. $(-\infty ,2]\cup [4,\infty )$
• C. $[-2,0]\cup [2,4]$
• D. $[0,2]$

Answer 1

The correct option is C $[-2,0]\cup [2,4]$

$|x-1|<3$
$\Rightarrow -2<x<4$
$|x-1|>1$
$\Rightarrow x>2$ or $x<0$
The common set is $[-2,0]\cup [2,4]$.