Question

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

• A. $[2,4]$
• B. $(-\infty ,2]\cup [4,+\infty )$
• C. $[-2,0]\cup [2,4]$
• D. none of these

Answer 1

Answer: (C)

$[-2,0]\cup [2,4]$

$|x-1|\le 3\Rightarrow x\in [-2,4]$

$|x-1|\ge 1$$\Rightarrow x\in (-\alpha ,0]\cup [2,\alpha )$

Both eqautions shoud be satisfied at the same time, so

$x\in [-2,0]\cup [2,4]$