You can put this solution on YOUR website! Since we are dealing with absolute value, equate 0 with +|2x-1| and -|2x-1|:
|2x-1| ≥ 0
2x-1 ≥ 0
2x ≥ 1
x ≥ ½
~and~
-|2x-1| ≥ 0
-2x+1 ≥ 0
-2x ≥ -1
x ≤ ½ (change of inequality symbol since you divided the terms with -1)
therefore, ½ ≤ x ≥ ½ , meaning, x ≠ ½ (any real number not equal to ½)
You can put this solution on YOUR website! By definition any absolute-value is non-negative, and thus there is no need for solving here: any real value of x is a solution of the inequality.
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