\(\left(x-3\right)\left(x-4\right)< 0.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3< 0.\\x-4>0.\end{matrix}\right.\\\left\{{}\begin{matrix}x-3>0.\\x-4< 0.\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 3.\\x>4.\end{matrix}\right.\\\left\{{}\begin{matrix}x>3.\\x< 4.\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow3< x< 4.\)
Vậy.....
\(\left(x-3\right)\left(x-4\right)< 0\)
\(\Rightarrow\left\{{}\begin{matrix}x-3>0\\x-4< 0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x-3< 0\\x-4>0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x>3\\x< 4\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x< 3\\x>4\end{matrix}\right.\)
\(\Rightarrow3< x< 4\)
Vậy 3 < x < 4