Write the set of values of x satisfying
Question:

Write the set of values of x satisfying |x − 1| ≤ 3 and |x − 1| ≥ 1.

Solution:

We have:

$|x-1| \leq 3$ and $|x-1| \geq 1$

We know,

$|x-a| \leq r \Rightarrow a-r \leq x \leq a+r$

$A$ nd, $|x-a| \geq r \Rightarrow x \leq a-r$ or $x \geq a+r$

$\therefore 1-3 \leq x \leq 1+3$ and $x \leq 1-1$ or $x \geq 1+1$

$\Rightarrow-2 \leq x \leq 4$ and $\mathrm{x} \leq 0$ or $x \geq 2$

$\Rightarrow x \in[-2,4]$ and $x \in(-\infty, 0] \cup[2, \infty)$

$\Rightarrow x \in[-2,0] \mathrm{U}[2,4]$

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