\(\left(x-3\right)\left(x-4\right)< 0.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3< 0.\\x-4>0.\end{matrix}\right.\\\left\{{}\begin{matrix}x-3>0.\\x-4< 0.\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 3.\\x>4.\end{matrix}\right.\\\left\{{}\begin{matrix}x>3.\\x< 4.\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow3< x< 4.\)
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