ĐKXĐ :
\(\left\{{}\begin{matrix}x\left(3x+1\right)\ge0\\x\left(x-1\right)\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\3x+1\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ge-\dfrac{1}{3}\end{matrix}\right.\Rightarrow x\ge0}\\\left\{{}\begin{matrix}x\le0\\3x+1\le0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le0\\x\le-\dfrac{1}{3}\end{matrix}\right.\Rightarrow x\le-\dfrac{1}{3}}\end{matrix}\right.\\\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\x-1\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ge1\end{matrix}\right.\Rightarrow x\ge1}\\\left\{{}\begin{matrix}x\le0\\x-1\le0\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}x\le0\\x\le1\end{matrix}\right.\Rightarrow x\le0\end{matrix}\right.\end{matrix}\right.\)
Vậy : x ≥ 1, x ≤ -1/3.
