\(x^2-3x=0\)
\(\Leftrightarrow x\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
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b/ \(x\left(x-2\right)< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\\x-2< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x< 0\\x-2>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\\x< 2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 0\\x>2\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}0< x< 2\\x\in\varnothing\end{matrix}\right.\)
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c/ \(\left(x+1\right)\left(x+4\right)>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\x+4>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\x+4< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\\x>-4\end{matrix}\right.\\\left\{{}\begin{matrix}x< -1\\x< -4\end{matrix}\right.\end{matrix}\right.\)
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