\(\dfrac{x+2}{3x+1}\le\dfrac{x-2}{2x-1}\)
\(\Leftrightarrow\dfrac{x+2}{3x+1}-\dfrac{x-2}{2x-1}\le0\)
\(\Leftrightarrow\left(x+2\right)\left(2x-1\right)-\left(x-2\right)\left(3x+1\right)\le0\)
\(\Leftrightarrow2x^2+3x-2-3x^2+5x+2\le0\)
\(\Leftrightarrow-x^2+8x\le0\)
\(\Leftrightarrow-x\left(x-8\right)\le0\)
\(\Leftrightarrow\left\{{}\begin{matrix}-x\le0\\x-8\ge0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\ge0\\x\ge8\end{matrix}\right.\) \(\Rightarrow x\ge8\)
\(\left\{{}\begin{matrix}-x\ge0\\x-8\le0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\le0\\x\le8\end{matrix}\right.\) \(\Rightarrow x\le0\)
tập nghiệm: \(x\ge8\) ; \(x\le0\)
