\(\dfrac{1-2x}{3-\left|x-1\right|}-3\le0\Leftrightarrow\dfrac{3\left|x-1\right|-2x-8}{3-\left|x-1\right|}\le0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge1\\\dfrac{3\left(x-1\right)-2x-8}{3-\left(x-1\right)}\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\\dfrac{3\left(1-x\right)-2x-8}{3-\left(1-x\right)}\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge1\\\dfrac{x-11}{4-x}\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\\dfrac{x+1}{x+2}\ge0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\\left[{}\begin{matrix}x< 4\\x\ge11\end{matrix}\right.\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\\left[{}\begin{matrix}x< -2\\x\ge-1\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}0\le x< 4\\x\ge11\end{matrix}\right.\\\left[{}\begin{matrix}x< -2\\-1\le x< 1\end{matrix}\right.\end{matrix}\right.\)
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