Question

giúp mk với ạ mk đag cần gấp trc 8h sáng ngày mai

a) (x - 2).(x + 3) ≤ 0

b) (3 - x).(x + 1) ≥ 0

c) \(\dfrac{2-x}{x-1}\)+ 2 ≤ 0

d)\(\dfrac{3x-3}{x-1}\) ^{< 2}

α \(\dfrac{2x-1}{x}\) >1

Answer 1

\(a,\left(x-2\right)\left(x+3\right)\le0.\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2\ge0.\\x+3\ge0.\end{matrix}\right.\\\left\{{}\begin{matrix}x-2\le0.\\x+3\le0.\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge2.\\x\ge-3.\end{matrix}\right.\\\left\{{}\begin{matrix}x\le2.\\x\le-3.\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\ge2.\\x\le-3.\end{matrix}\right.\)

​​\(b,\left(3-x\right)\left(x+1\right)\ge0.\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3-x\ge0.\\x+1\ge0.\end{matrix}\right.\\\left\{{}\begin{matrix}3-x\le0.\\x+1\le0.\end{matrix}\right.\end{matrix}\right.\) 

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le3.\\x\ge-1.\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge3.\\x\le-1.\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow-1\le x\le3.\)

\(c,\dfrac{2-x}{x-1}+2\le0.\\ \left(x\ne1\right)\\ \Leftrightarrow\dfrac{2-x+2x-2}{x-1}\le0.\\ \Leftrightarrow\dfrac{x}{x-1}\le0.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le0.\\x\le1.\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge0.\\x\ge1.\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\le0.\\x\ge1.\end{matrix}\right.\)