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  4. The set of values of x satisfying 2 ≤|x-3|<4 is

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Q. The set of values of $x$ satisfying $2 \leq|x-3|<4$ is

Linear Inequalities

Solution:

We have, $2 \leq|x-3|<4$
Case I If $x< 3$, then
$ 2 \leq|x-3|<4 $
$\Rightarrow 2 \leq-(x-3)<4 $
$ \Rightarrow 2 \leq-x+3<4$
Subtracting 3 from both sides,
$-1 \leq-x< 1$
Multiplying $(-1)$ on both sides,
$-1< x \leq 1 $
$\Rightarrow x \in(-1,1]$
Case II If $x>3$, then
$ 2 \leq|x-3|<4$
$ \Rightarrow 2 \leq x-3<4$
Adding 3 on both sides,
$\Rightarrow 5 \leq x<7$
Hence, the solution set of given inequality is $x \in(-1,1] \cup[5,7)$