Question

Tìm x \(\in\)Q

(2x + 5) . (4 - \(\dfrac{1}{2}\)x) < 0

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Answer 1

\(\left(2x+5\right).\left(4-\dfrac{1}{2}x\right)< 0\)

\(\Rightarrow\left\{{}\begin{matrix}2x+5>0\\4-\dfrac{1}{2}x< 0\end{matrix}\right.\) hay \(\left\{{}\begin{matrix}2x+5< 0\\4-\dfrac{1}{2}x>0\end{matrix}\right.\)

+, Xét \(\left\{{}\begin{matrix}2x+5>0\\4-\dfrac{1}{2}x< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x>-5\\\dfrac{1}{2}x>4\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x>\dfrac{-5}{2}\\x>8\end{matrix}\right.\Rightarrow x>8\)

+, Xét \(\left\{{}\begin{matrix}2x+5< 0\\4-\dfrac{1}{2}x>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x< -5\\\dfrac{1}{2}x< 4\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x< -\dfrac{5}{2}\\x< 8\end{matrix}\right.\) \(\Rightarrow x< -\dfrac{5}{2}\)

Vậy \(x>8\) hoặc \(x< -\dfrac{5}{2}\) thoả mãn yêu cầu đề bài.

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