Question

(5-x).(7-x) < 0

Answer 1

\(\left(5-x\right)\left(7-x\right)< 0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}5-x>0\\7-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}5-x< 0\\7-x>0\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 5\\x>7\end{matrix}\right.\\\left\{{}\begin{matrix}x>5\\x< 7\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow5< x< 7\)