\(\left(x-2\right)\left(x-3\right)< 0\\ \Rightarrow\left(x-2\right)\text{ và }\left(x-3\right)\text{khác dấu}\)
\(\left\{{}\begin{matrix}x-2>0\\x-3< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>2\\x< 3\end{matrix}\right.\Rightarrow2< x< 3\\ \left\{{}\begin{matrix}x-2< 0\\x-3>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 2\\x>3\end{matrix}\right.\left(loai\right)\)
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\(x\cdot x-2x>0\Rightarrow x\left(x-2\right)>0\Rightarrow x\text{ và }x-2\text{ cùng dấu}2\)
\(\left\{{}\begin{matrix}x>0\\x-2>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>0\\x>2\end{matrix}\right.\Rightarrow x>2\\ \left\{{}\begin{matrix}x< 0\\x-2< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 0\\x< 2\end{matrix}\right.\Rightarrow x< 2\)
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\(x\cdot x-5x< 0\Rightarrow x\left(x-5\right)< 0\Rightarrow x\text{ và }x-5\text{ khác dấu}\)
\(\left\{{}\begin{matrix}x>0\\x-5< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>0\\x< 5\end{matrix}\right.\Rightarrow0< x< 5\\ \left\{{}\begin{matrix}x< 0\\x-5>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 0\\x>5\end{matrix}\right.\left(loai\right)\)
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