1.
\(\left(x-1\right)\left(2-3x\right)< 0\Leftrightarrow\left[{}\begin{matrix}x>1\\x< \dfrac{2}{3}\end{matrix}\right.\) \(\Rightarrow x\in\left(-\infty;\dfrac{2}{3}\right)\cup\left(1;+\infty\right)\)
2.
\(\dfrac{1-7x}{x\left(x+1\right)}\ge0\Leftrightarrow\left[{}\begin{matrix}x< -1\\0< x\le\dfrac{1}{7}\end{matrix}\right.\) \(\Rightarrow x\in\left(-\infty;-1\right)\cup(0;\dfrac{1}{7}]\)
3.
\(x\left(x-2\right)\left(4-2x\right)\le0\Leftrightarrow-2x\left(x-2\right)^2\le0\)
\(\Leftrightarrow2x\left(x-2\right)^2\ge0\Rightarrow x\ge0\)
\(\Rightarrow x\in[0;+\infty)\)
4.
\(\dfrac{2x\left(3x-1\right)}{6-3x}\le0\Leftrightarrow\dfrac{x\left(3x-1\right)}{2-x}\le0\Rightarrow\left[{}\begin{matrix}0\le x\le\dfrac{1}{3}\\x>2\end{matrix}\right.\)
\(\Rightarrow x\in\left[0;\dfrac{1}{3}\right]\cup\left(2;+\infty\right)\)
Giải bpt sau :
