\(\left|3x-1\right|-x=5\Leftrightarrow\left|3x-1\right|=5+x\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=5+x\\3x-1=-5-x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\4x=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
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