Question

Tìm x

(2x-1)(3-x)>0

Answer 1

\(\left(2x-1\right)\left(3-x\right)>0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1>0\\3-x>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1< 0\\3-x< 0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\frac{1}{2}\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< \frac{1}{2}\\x>3\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\frac{1}{2}< x< 3\)

Answer 2

\(\left(2x-1\right).\left(3-x\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1>0\\3-x>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1< 0\\3-x< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\frac{1}{2}\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< \frac{1}{2}\\x>3\end{matrix}\right.\end{matrix}\right.\)

Answer 3

\(\left(2x-1\right)\left(3-x\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1>0\\3-x>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1< 0\\3-x< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\frac{1}{2}\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< \frac{1}{2}\\x>3\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\in\frac{1}{2},3\\x\in\varnothing\end{matrix}\right.\)