Question

Bài 1. Giải các bất phương trình:

a) \(\dfrac{2x-1}{x-2}< \dfrac{1}{4x+2}\)

b) \(\left|x^2+5x+4\right|>x^2+3x-4\)

c) \(\dfrac{x+2}{3}-x+1>x+3\)

d) \(\dfrac{3x+5}{2}-1\le\dfrac{x+2}{3}+x\)

Bài 2. Xét dấu các biểu thức:

a) \(f\left(x\right)=\left(x-3\right)\left(2x+3\right)\)

b) \(g\left(x\right)=\left(-2x+3\right)\left(x-2\right)\left(x+4\right)\)

c) \(h\left(x\right)=\dfrac{\left(x+2\right)\left(4-x\right)}{3-2x}\)

d) \(k\left(x\right)=\dfrac{2}{3-x}-\dfrac{1}{3+x}\)

Answer 1

1:

c: =>1/3x+2/3-x+1>x+3

=>-2/3x+5/3-x-3>0

=>-5/3x-4/3>0

=>-5x-4>0

=>x<-4/5

d: =>3/2x+5/2-1<=1/3x+2/3+x

=>3/2x+3/2<=4/3x+2/3

=>1/6x<=2/3-3/2=-5/6

=>x<=-5

2: