\(a)x\left(x-2\right)< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x< 2\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>0\\x< 2\end{matrix}\right.\)
\(b)\left(x+1\right)\left(2x-6\right)< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1< 0\\2x-6>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1>0\\2x-6< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< -1\\x>3\end{matrix}\right.\\\left\{{}\begin{matrix}x>-1\\x< 3\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>-1\\x< 3\end{matrix}\right.\)
