\(\left(x+3\right)\left(2x-4\right)< 0\)
TH1: \(\left\{{}\begin{matrix}x+3>0\\2x-4< 0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>-3\\x< 2\end{matrix}\right.\) \(\Leftrightarrow-3< x< 2\)
TH2: \(\left\{{}\begin{matrix}x+3< 0\\2x-4>0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x< -3\\x>2\end{matrix}\right.\)\(\Leftrightarrow x\in\varnothing\)
Vậy \(-3< x< 2\)
Có: (x + 3)(2x - 4) < 0 \(\Leftrightarrow\) x + 3 và 2x - 4 trái dấu
+) Xét: x + 3 < 0 => x < -3
2x - 4 > 0=> x > 2
=> 2 < x < -3 (vô lí) => loại
+) Xét: x + 3 > 0 => x > -3
2x - 4 < 0 => x < 2
=> -3 < x < 2 (tm)
Vậy...
