\(\left(x-1\right)\left(1-9x^2\right)>=0\)
=>\(\left(x-1\right)\left(9x^2-1\right)< =0\)
TH1: \(\left\{{}\begin{matrix}x-1>=0\\9x^2-1< =0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=1\\x^2< =\dfrac{1}{9}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=1\\-\dfrac{1}{3}< =x< =\dfrac{1}{3}\end{matrix}\right.\)
=>\(x\in\varnothing\)
TH2: \(\left\{{}\begin{matrix}x-1< =0\\9x^2-1>=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< =1\\x^2>=\dfrac{1}{9}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< =1\\\left[{}\begin{matrix}x>=\dfrac{1}{3}\\x< =-\dfrac{1}{3}\end{matrix}\right.\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\dfrac{1}{3}< =x< =1\\x< =-\dfrac{1}{3}\end{matrix}\right.\)
