\(\left|x+1\right|+\left|x-5\right|=3x+1\left(đk:x\ge-\dfrac{1}{3}\right)\)
\(\Leftrightarrow x+1+\left|x-5\right|=3x+1\)
\(\Leftrightarrow\left|x-5\right|=2x\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=2x\left(x\ge5\right)\\x-5=-2x\left(-\dfrac{1}{3}\le x< 5\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\left(ktm\right)\\x=\dfrac{5}{3}\left(tm\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}-x-1+5-x=3x+1\left(x< -1\right)\\x+1+5-x=3x+1\left(-1\le x< 5\right)\\x+1+x-5=3x+1\left(x\ge5\right)\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\left(ktm\right)\\x=\dfrac{5}{3}\left(tm\right)\\x=-5\left(ktm\right)\end{matrix}\right.\Rightarrow x=\dfrac{5}{3}\)