Answer
$|2x-1|=2x-1 ≥0.5 $
and
$-(2x-1)<0.5$
Work Step by Step
For $x =0 $ or $x> 0,| x| = x$
For $x< 0,| x| = -x$
Now, apply the above definition for the expression $|2x-1|$.
$|2x-1|>0$ if $x> 0.5$ and $2x-1 < 0$ if $x<0.5$.
Therefore,
$|2x-1|=2x-1 ≥0.5 $
and
$-(2x-1)<0.5$