APPENDIX A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 10

$|2x-1|=2x-1 ≥0.5 $ and $-(2x-1)<0.5$

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 $-(2x-1)<0.5$