g: \(x^2-7x+12>=0\)
=>(x-3)(x-4)>=0
TH1: \(\left\{{}\begin{matrix}x-3>=0\\x-4>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=3\\x>=4\end{matrix}\right.\Leftrightarrow x>=4\)
TH2: \(\left\{{}\begin{matrix}x-3< =0\\x-4< =0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =3\\x< =4\end{matrix}\right.\Leftrightarrow x< =3\)
h: \(2x^2+9x+10< =0\)
=>(x+2)(2x+5)<=0
=>\(-\dfrac{5}{2}< =x< =-2\)
i: \(\left(x+2\right)\left(2x^2+4\right)\left(x-1\right)< =0\)
=>(x+2)(x-1)<=0(Vì \(2x^2+4>=4>0\forall x\))
TH1: \(\left\{{}\begin{matrix}x+2< =0\\x-1>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =-2\\x>=1\end{matrix}\right.\Leftrightarrow x\in\varnothing\)
TH2: \(\left\{{}\begin{matrix}x+2>=0\\x-1< =0\end{matrix}\right.\Leftrightarrow-2< =x< =1\)
a: (x+2)(x-3)>0
TH1: \(\left\{{}\begin{matrix}x+2>0\\x-3>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>-2\\x>3\end{matrix}\right.\)
=>x>3
TH2: \(\left\{{}\begin{matrix}x+2< 0\\x-3< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< -2\\x< 3\end{matrix}\right.\)
=>x<-2
b: (x+1)(2x+1)>=0
TH1: \(\left\{{}\begin{matrix}x+1>=0\\2x+1>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-1\\x>=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow x>=-\dfrac{1}{2}\)
TH2: \(\left\{{}\begin{matrix}x+1< =0\\2x+1< =0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =-1\\x< =-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow x< =-1\)
c: (2x-3)(x+5)<0
TH1: \(\left\{{}\begin{matrix}2x-3< 0\\x+5>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< \dfrac{3}{2}\\x>-5\end{matrix}\right.\Leftrightarrow-5< x< \dfrac{3}{2}\)
Th2: \(\left\{{}\begin{matrix}2x-3>0\\x+5< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>\dfrac{3}{2}\\x< -5\end{matrix}\right.\Leftrightarrow x\in\varnothing\)
d: ĐKXĐ: \(x\ne\dfrac{3}{2}\)
\(\dfrac{x-4}{2x-3}>0\)
TH1: \(\left\{{}\begin{matrix}x-4>0\\2x-3>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>4\\x>\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow x>4\)
TH2: \(\left\{{}\begin{matrix}x-4< 0\\2x-3< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< 4\\x< \dfrac{3}{2}\end{matrix}\right.\Leftrightarrow x< \dfrac{3}{2}\)
e: ĐKXĐ: \(x\ne-1\)
\(\dfrac{x+3}{x+1}< =0\)
TH1: \(\left\{{}\begin{matrix}x+3< =0\\x+1>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =-3\\x>-1\end{matrix}\right.\Leftrightarrow x\in\varnothing\)
TH2: \(\left\{{}\begin{matrix}x+3>=0\\x+1< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-3\\x< -1\end{matrix}\right.\Leftrightarrow-3< =x< -1\)
f: ĐKXĐ: x<>-3/4
\(\dfrac{x-1}{4x+3}>=0\)
TH1: \(\left\{{}\begin{matrix}x-1>=0\\4x+3>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=1\\x>-\dfrac{3}{4}\end{matrix}\right.\Leftrightarrow x>=1\)
TH2: \(\left\{{}\begin{matrix}x-1< =0\\4x+3< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =1\\x< =-\dfrac{3}{4}\end{matrix}\right.\Leftrightarrow x< =-\dfrac{3}{4}\)
