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Esercizi svolti su disequazioni fratte, esponenziali, logaritmiche, irrazionali, …

1. $(x+3(x-1))/(2/3)-(x+2)(x-1/3)>1/4-x^2$

2. $5x-6(x-1)>(x-3)(x+3)-(x-2)(x+2)$

3. $(x+2)(x-2)-(x+1/2)^2>=1/2(x-1)$

4. $(x-1/3)(x+2/5)-(x-2)(x+3) lt 4/15$

5. $(x+1)^2-(3x+4)1/2-4(x+1)-x^2>0$

6. $(4x-1)x-43)$

7. $x/5-(x+1/3)/4 lt 1/5-2(x-1/3)$

8. $1/3(x-(14)/3)-1/4((6x-11)/3) lt 3/2x$

9. $(x+5)(x+3)>(x+9)(x+1)$

10. $2/3x>=5/4x+7/(15)$

11. $(x+1)^2>[6-(2-3x)]1/3x-3$

12. $(10x+1)^24(4x+1)^2 lt (6x+1)^2$

13. $(3x+1)^2-4x(x-2)>5x(x+6)$

14. $(x+1)^2-2$

15. $1/3[x-(1+(25)/(12))]-2/3(1-3x)>x$

16. $(x-1/2)(x+2/4)-(x-3)(x+5) lt 4/8$

17. $(3x+1)/4-(x+5)/3 lt =1-(x+2)/6$

18. $(2x-1)/3-(x-1)/4>(x+2)/5-1/2$

19. $(1+2x)(1-3x)(2+x)(1-2x)>0$

20. $x^2-3x+2=(x-2)(x-1) > 0$

21. $log_(1/3)(x^2–2x)>=-1$

22. $3*9^x-4*3^x+1 lt 0$

23. $x^2-4x+4-a^2 lt 0$

24. $sqrt(-x^2-x+6)>x+3$

25. $3x-3>0$

26. $(x^3–3)>0$

27. $cos(2x)+cosx$

28. $log(1/2+x^2)>0$

29. $(|2x-3|)/(2+|3x|)>0$

30. $(2(1-x))/3+1/2 lt x-x/2-(2+3x)/2$

31. $(log_2(|x|))^2+2log_2(|x|)-3 lt 0$

32. $x(a-2)>a(a-2)$

33. $3sinx+sqrt(3)sinx lt sqrt(3)$

34. $log(2x-1)+log(3x-8)-logx-log(x-2)>log5-log3$

35. ${((3x^4(x+1)^3)/(x^2+1)^2 lt 0),(((x^2-3x)^5)/(2x(x-1)^2) >=0):}$

36. $|(2+|x|)/(3+|x|)|>1/2$

37. $|(2x+5)/(4x-2)-(x-1)/(1-2x)| lt 2/3$

38. $sqrt(x^2+2)-sqrt(3x-1)>4x$

39. $2*5^x+4*5^(3-x) lt 205$

40. $(1-2x)(3-2x)(1-4x)>0$

41. $(x+|x-1|+3-2(x-3))/(|x|-|x^2-1|)>=0$

42. $(x^2-4x+4)/(3x^2-5x+2) >0$

43. $(1-x)/(1+x) > 1$

44. $|3x-1| lt = 2x-3$

45. $a(x-1)-5 lt = 3x-a$

46. $4[(x-2)/(3)-2((x-1)/(6)-(1-x)/(9))] lt x-8$

47. $1-3/(x+2))$

48. $1/sqrt(sinx+2)+1/(sinx+cosec(pi/6))>0$

49. $ln^2x-sqrt(5lnx)>0$

50. $ln^2x-root(5)(lnx)>0$