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  4. The set of real values of x satisfying |x-1| ≤ 3 and |x-1| ≥ 1 is

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Q. The set of real values of $x$ satisfying $|x-1| \leq 3$ and $|x-1| \geq 1$ is

Linear Inequalities

Solution:

$| x -1| \leq 3 $
$\Rightarrow -3 \leq x -1 \leq 3$
$ \Rightarrow -2 \leq x \leq 4$
and $| x -1| \geq 1 $
$\Rightarrow x -1 \leq-1$ or $x -1 \geq 1$
$\Rightarrow x \leq 0$ or $x \geq 2$
Taking the common values of $x$, we get
$x \in[-2,0] \cup[2,4]$