We have the following:
[tex]|2x-1|=2x-1[/tex]solving for x:
[tex]\begin{gathered} |2x-1|=2x-1 \\ -(2x-1)=2x-1\rightarrow-2x+1=2x-1 \\ 2x+2x=1+1 \\ 4x=2 \\ x=\frac{2}{4}=\frac{1}{2} \\ (2x-1)=2x-1\rightarrow2x-1=2x-1 \\ 0=0 \\ \text{True for all x} \end{gathered}[/tex]Therefore, the answer is:
[tex]x\ge\frac{1}{2}[/tex]