Tìm x biết (3x + 1 ) ( 2x - 4 ) < 0

a) (3x+1)(2x-4) <0

\(\Rightarrow\)3x+1 và 2x-4 trái dấu

Th1: \(\left\{\begin{matrix}3x+1>0\\2x-4< 0\end{matrix}\right.\)

\(\Rightarrow\left\{\begin{matrix}3x>-1\\2x< 4\end{matrix}\right.\)

\(\Rightarrow\left\{\begin{matrix}x>\frac{-1}{3}\\x< 2\end{matrix}\right.\Rightarrow\frac{-1}{3}< x< 2\)

Th2: \(\left\{\begin{matrix}3x+1< 0\\2x-4>0\end{matrix}\right.\)

\(\Rightarrow\left\{\begin{matrix}3x< -1\\2x>4\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x< \frac{-1}{3}\\x>2\end{matrix}\right.\Rightarrow x\in\varnothing\)

b)(-x-5)(2x+1)>0

=> -x-5 và 2x+1 cùng dấu

TH1: \(\left\{\begin{matrix}-x-5>0\\2x+1>0\end{matrix}\right.\Rightarrow\left\{\begin{matrix}-x>5\\2x>-1\end{matrix}\right.\)

\(\Rightarrow\left\{\begin{matrix}x< -5\\x>\frac{-1}{2}\end{matrix}\right.\Rightarrow x\in\varnothing\)

Th2: Tương tự vs -x-5<0 và 2x+1<0

=>x<-5

c) tương tự câu a)

d)\(\left|x+3\right|< 5\)

Th1: x+3<5

=> x<2

Th2: -(x+3)<5

=> -x-3<5

=> -x<8

=> x<-8

e)\(\left|2x-3\right|< 1\)

Th1: 2x-3<1 => 2x<4 => x<2

Th2: -(2x-3)<1 =>-2x+3<1

=> -2x<-2

=>x<1