\(\left|x-2\right|+3x=8\)
\(\Leftrightarrow\left|x-2\right|=8-3x\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=8-3x\\x-2=-\left(8-3x\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=8-3x\\x-2=-8+3x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}4x=10\\-2x=-6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=3\end{matrix}\right.\)