$|3x-1|=|x+1|$
⇒ \(\left[ \begin{array}{l}3x-1=x+1\\3x-1=-x-1\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}3x-x=1+1\\3x+x=-1+1\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}2x=2\\4x=0\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=1\\x=0\end{array} \right.\)
Vậy $x=1$ hoặc $x=0$