Question

\(\dfrac{1}{1-x}\ge2\)

Answer 1

\(\dfrac{1}{1-x}\ge2=>2\left(1-x\right)\le1\\ =>2-2x\le1\\ =>2x\le1\\ =>x\le\dfrac{1}{2}\)

Answer 2

\(\dfrac{1}{1-x}-2\ge0\Leftrightarrow\dfrac{1-2+2x}{1-x}\ge0\Leftrightarrow\dfrac{2x-1}{x-1}\le0\)

TH1 : \(\left\{{}\begin{matrix}2x-1< 0\\x-1>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< \dfrac{1}{2}\\x>1\end{matrix}\right.\)( vô lí ) 

TH2 : \(\left\{{}\begin{matrix}2x-1>0\\x-1< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>\dfrac{1}{2}\\x< 1\end{matrix}\right.\Leftrightarrow\dfrac{1}{2}< x< 1\)