Задачи по школьной математике. Неравенства с модулем II

Неравенства с модулем II

  1. |x-4|<0,1
  2. |x-4|>0,2
  3. |x+3|<1
  4. |x+3|>1
  5. |x+2|<0,5
  6. |x+2|>0,5
  7. |2x-5|<1
  8. |2x-5|>1
  9. |x-1|<2x-5
  10. 3x>2-|3-x|
  11. 5x-7<|x+2|
  12. |5x-3|>6x-2
  13. |x-3|>2x
  14. |4x+2|>5x+3
  15. |2x-2|>3x+2
  16. |x^2+x-20|\leq x^2+x-20
  17. 3x^2-|10x-3|>0
  18. |2x^2-x-10|>|x^2-8x-22|
  19. \displaystyle|\frac{3-2x}{1+x}|<2
  20. \displaystyle|\frac{2x+3}{5x-2}|<3
  21. -\displaystyle\frac{2}{|x|+1}\geq |x|-2
  22. \displaystyle\frac{5}{|3-x|+4}>|3-x|
  23. |2x+1|+|3x+2|\leq 5x+3
  24. |2-5x|+|x+1|\geq x+3
  25. |x-1|\leq |2x-3|-|x-2|
  26. |5x-1|-|4x+2|\leq |x-3|
  27. |2x+5|+|3x-7|>|4x+1|
  28. x^2+|x-1|\leq 5
  29. |x+2|+3-x^2\leq 0
  30. |x^2-3|+x^2+x<7
  31. |2x-|x-2||<3
  32. ||3x+1|+x+1|\geq 2
  33. |2x+1-|3x+1||\leq x+2
  34. |x^2-|x^2+x||>11
  35. ||2x^2-x|-3|\leq2x^2+x+5
  36. ||x^3-x-1|-5|\geq x^3+x+8
  37. |\sqrt{x+2}-\sqrt{x+3}|\leq 1

Ответы

  1. (3,9; 4,1)
  2. (-\infty; 3,8)\cup (4,2; +\infty)
  3. (-4; -2)
  4. (-\infty; -4)\cup (-2;+\infty)
  5. (-2,5; -1,5)
  6. (-\infty; -2,5)\cup (-1,5; +\infty)
  7. (2; 3)
  8. (-\infty; 2)\cup (3;+\infty)
  9. (4; +\infty)
  10. (-0,5; +\infty)
  11. (-\infty; 2,25)
  12. (-\infty; 5/11)
  13. (-\infty; 1)
  14. (-\infty; -5/9)
  15. (-\infty; 0)
  16. (-\infty; -5]\cup [4;+\infty)
  17. (-\infty; (-5-\sqrt{34})/3)\cup ((-5+\sqrt{34})/3; 1/3)\cup (3; +\infty)
  18. (-\infty; -4)\cup (-3; (9-\sqrt{465})/6)\cup ((9+\sqrt{465})/6; +\infty)
  19. (1/4; +\infty)
  20. (-\infty; 3/17)\cup (9/13; +\infty)
  21. [-1; 1]
  22. (2;4)
  23. [-1/2; +\infty)
  24. (-\infty; 0]\cup [4/5; +\infty)
  25. (-\infty; 1]\cup [2; +\infty)
  26. (-\infty; +\infty)
  27. (-\infty; 2,2)\cup (3; +\infty)
  28. [(1-\sqrt{17})/2; 2]
  29. (-\infty; (1-\sqrt{21})/2]\cup [(1+\sqrt{21})/2; +\infty)
  30. (-5/2; 2)
  31. (-1/3; 5/3)
  32. (-\infty; -1]\cup [0; +\infty)
  33. [-2/3; +\infty)
  34. (-\infty; -11)\cup (11; +\infty)
  35. [-4; +\infty)
  36. (-\infty; -\sqrt[3]{6}]
  37. [-2; +\infty)