Ta có: \(\left(3x+5\right).\left(x-4\right)< 0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x-5>0\\x-4< 0\end{matrix}\right.\\\left\{{}\begin{matrix}3x-5< 0\\x-4>0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\dfrac{5}{3}\\x< 4\end{matrix}\right.\\\left\{{}\begin{matrix}x< \dfrac{5}{3}\\x>4\end{matrix}\right.\end{matrix}\right.\)
Trường hợp 1: Nếu x > \(\dfrac{5}{3}\) và x < 4
Suy ra \(x\in\left\{2;3\right\}\)
Trường hợp 2: Nếu x < \(\dfrac{5}{3}\) và x > 4
Suy ra x ∈ ∅
Vậy \(x\in\left\{2;3\right\}\)
