Question

[Nghiêm Trần Mai Nguyên]

Tìm tham số m để:

a, (-∞; 2m+1)⊂(-∞; 1)

b,\((-\infty;2-3m]\cap[2;+\infty)=\varnothing\)

c, \(\left[-1;3\right]\cap\left(2m-5;2m+4\right)=\varnothing\)

Answer 1

[Nguyễn Việt Lâm]

a.

\(\left(-\infty;2m+1\right)\subset\left(-\infty;1\right)\Rightarrow2m+1\le1\)

\(\Rightarrow m\le0\)

b.

\((-\infty;2-3m]\cap[2;+\infty)=\varnothing\Rightarrow2-3m< 2\)

\(\Rightarrow m>0\)

c.

\(\left[-1;3\right]\cap\left(2m-5;2m+4\right)=\varnothing\Rightarrow\left[{}\begin{matrix}2m-5\ge3\\2m+4\le-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}m\ge4\\m\le-\dfrac{5}{2}\end{matrix}\right.\)