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

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Answer 1 · 2018-06-12T13:01:12

$0 < x < 2$ $0< x <2$

For $x \geq 2$ $x>=2$ we have

$x - 2 < 2$ $x-2<2$

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

$2 \leq x < 4$ $2<=x<4$

if $x < 2$ $x<2$ we have

$- x + 2 < 2$ $-x+2<2$
so

$- x < 0$ $-x<0$

or

$x > 0$ $x>0$

so we get for this inequality

$0 < x < 2$ $0 < x <2$

How do you solve |x−2|<2|x-2|<2?