\(\left|x-1\right|=x\)
\(\Rightarrow\)\(\left[{}\begin{matrix}x-1=x\\x-1=-x\end{matrix}\right.\)
\(\Rightarrow\)\(\left[{}\begin{matrix}x=1+x\left(loại\right)\\x+x=1\end{matrix}\right.\)
\(\Rightarrow2x=1\)
\(x=1:2\)
\(x=\frac{1}{2}\)
Vậy \(x=\frac{1}{2}\)