How do you solve $|x-2|<2$ ?

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Answer 1 · 2018-06-12T13:01:12

$0< x <2$

For $x>=2$ we have

$x-2<2$

$x<4$
and in the first case we obtain

$2<=x<4$

if $x<2$ we have

$-x+2<2$
so

$-x<0$

or

$x>0$

so we get for this inequality

$0 < x <2$

How do you solve |x-2|<2|x-2|<2?