Bài 1 : Giải bất phương trình sau

1 , \(\left(2x+3\right)\left(5x-7\right)\ge0\)

2 , \(\left(3-2x\right)\left(4x+3\right)< 0\)

3 , \(\left(2x+5\right)\left(3-x\right)\left(5x-1\right)\le0\)

4 , \(x^2-3x+2< 0\)

5 , \(-x^2+12x+13>0\)

6 , \(x^2+6x+9\le0\)

7 , \(\frac{x+2}{3x+1}>\frac{x-2}{2x-1}\)

8 , \(\frac{1}{x+2}< \frac{3}{x-3}\)

9 , \(\frac{5x-6}{2x-5}\le6\)

10 , \(\left(x+1\right)\left(x-1\right)\left(3x-6\right)>0\)

Bài 2 : Giải các bất phương trình sau :

11 , \(\left(2x-7\right)\left(4-5x\right)\ge0\)

12 , \(x^2-x-20>2\left(x-11\right)\)

13 , \(3x\left(2x+7\right)\left(9-3x\right)\ge0\)

14 , \(x^3+8x^2+17x+10< 0\)

15 , \(x^3+6x^2+11x+6>0\)

16 , \(\frac{\left(2x-5\right)\left(x+2\right)}{-4x+3}>0\)

17 , \(\frac{x-3}{x+1}>\frac{x+5}{x-2}\)

18 , \(\frac{x-3}{x+5}< \frac{1-2x}{x-3}\)

19 , \(\frac{3x-4}{x-2}>1\)

20 , \(\frac{2x-5}{2-x}\ge-1\)

1)2x(25x-4)-(5x-2)(5x+1)=8 / 5)\(2\left(x-2\right)-3\left(3x-1\right)=\left(x-3\right)\)

2)x(4x-3)-(2x-2)(2x-1)=5 / 6)\(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

3)\(\frac{5}{2x+3}+\frac{3}{9-x^2}=\frac{8}{7\left(x=3\right)}\) / 7)\(\frac{5x-2}{6}+\frac{3-4x}{2}=2-\frac{x+7}{3}\)

4)\(\frac{2}{3\left(x-2\right)}+\frac{5}{12-3x^2}=\frac{3}{4\left(x+2\right)}\) / 8)\(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

Giải các bất phương trình sau:

a) \(\frac{x^2-9x+14}{x^2+9x+14}\ge0\)

b) \(\frac{x^2+1}{x^2+3x-10}< 0\)

c) \(\frac{10-x}{5+x^2}>\frac{1}{2}\)

d) \(\frac{x+1}{x-1}+2>\frac{x-1}{x}\)

e) \(\frac{1}{x+1}+\frac{2}{x+3}\le\frac{3}{x+2}\)

f) \(\frac{x-3}{x+1}-\frac{x-2}{x-1}\le\frac{x^2+4x+15}{x^2-1}\)

g) \(\frac{x^2-4x+3}{x^2-2x}\ge0\)

h) \(\frac{x+2}{3x+1}\le\frac{x-2}{2x-1}\)

i) \(\frac{11x^2-5x+6}{x^2+5x+6}\le x\)

j) \(\frac{\left(1-2x\right)\left(\sqrt{3}x+1\right)}{2\sqrt{2}x-1}\ge0\)

k) \(\frac{\left(5x+1\right)-\left(7x-2\right)}{\left(-x^2-1\right)\left(x^2-4x+4\right)}\le0\)

l) \(\frac{1}{x^2-7x+5}\ge\frac{1}{x^2+2x+5}\)

m) \(\frac{\left(x-1\right)\left(x^3-1\right)}{x^2+\left(1+2\sqrt{2}\right)x+2+\sqrt{2}}\le0\)

Bài 2: Xét sự tương đương của các cặp BPT sau

a, \(4x-6+\frac{1}{x-2}\ge2+\frac{1}{x-2}\) và \(4x-8\ge0\)

b, \(3x-2+\frac{1}{x-3}\ge1+\frac{1}{x-3}\) và \(3x-3\ge0\)

c, \(x+4\ge0\) và \(\left(x-1\right)^2\left(x+4\right)>0\)

d,\(\left(x^2-4x+5\right)\left(x-5\right)>0\) và \(x-5>0\)

e, \(x-12\ge0\) và \(\left(x-2\right)^2\ge0\)

f, \(\sqrt{\left(x-1\right)\left(x-2\right)}\ge x\) và \(\sqrt{x-1}.\sqrt{x-2}\ge x\)

Bài 3. Giải bất phương trình

a, \(|5x – 3| &lt; 2\)

b, \(\left|3x-2\right|\ge6\)

c, \(\left|2x-1\right|\le x+2\)

d, \(\left|3x+7\right|>2x+3\)

e, \(\sqrt{x-3}\ge\sqrt{3-x}\)

f, \(\sqrt{x-1}< 3+\sqrt{x-1}\)

g, \(\frac{x-2}{\sqrt{x-4}}\ge\frac{4}{\sqrt{x-4}}\)

h, \(\left(x+5\right)\sqrt{\left(x-3\right)\left(x^2-10x+25\right)}>0\)