a \(\Rightarrow\left[{}\begin{matrix}x+3>0;x-2>0\\x+3< 0;x-2< 0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x>-3;x>2\\x< -3;x< 2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x>2\\x< -3\end{matrix}\right.\)
b \(\Rightarrow\left[{}\begin{matrix}2x+5>0;x+1< 0\\2x+5< 0;x+1>0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x>-\dfrac{5}{2};x< -1\\x< -\dfrac{5}{2};x>-1\left(L\right)\end{matrix}\right.\) \(\Rightarrow-\dfrac{5}{2}< x< -1\)
c \(\Rightarrow x-1\ge0;x-5\le0\) (vì x-5<x-1)\(\Rightarrow1\le x\le5\)
d \(\Rightarrow\left[{}\begin{matrix}2x+3\ge0;x-1\ge0\\2x+3\le0;x-1\le0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x\ge-\dfrac{3}{2};x\ge1\\x\le-\dfrac{3}{2};x\le1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x\ge1\\x\le-\dfrac{3}{2}\end{matrix}\right.\)
a) Ta có: (x+3)(x-2)>0
\(\Leftrightarrow\left[{}\begin{matrix}x-2>0\\x+3< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>2\\x< -3\end{matrix}\right.\)
b) Ta có: \(\left(2x+5\right)\left(x+1\right)< 0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+5>0\\x+1< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>-\dfrac{5}{2}\\x< -1\end{matrix}\right.\Leftrightarrow-\dfrac{5}{2}< x< -1\)
c) Ta có: \(\left(x-1\right)\left(x-5\right)\le0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1\ge0\\x-5\le0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x\le5\end{matrix}\right.\Leftrightarrow1\le x\le5\)
d) Ta có: \(\left(2x+3\right)\left(x-1\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+3\le0\\x-1\ge0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\le-\dfrac{3}{2}\\x\ge1\end{matrix}\right.\)
