\(\left\{{}\begin{matrix}2x-1>x+1\\2x-1>m\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x>2\\2x-1>m\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}2x>4\\2x-1>m\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}2x-1>3\\2x-1>m\end{matrix}\right.\)
\(\Rightarrow m\le3\)
\(\left\{{}\begin{matrix}2x-1>x+1\\2x-1>m\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x>2\\x>\dfrac{m+1}{2}\end{matrix}\right.\)
Để bpt có nghiệm thì: \(\left[{}\begin{matrix}\dfrac{m+1}{2}>2\\\dfrac{m+1}{2}=2\\\dfrac{m+1}{2}< 2\end{matrix}\right.\) \(\Leftrightarrow\) \(\left[{}\begin{matrix}m>3\\m=3\\m< 3\end{matrix}\right.\) \(\Leftrightarrow\) \(m\in R\)
Vậy với mọi giá trị của m thì bpt có nghiệm
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