МГУ Неравенства с модулем

Неравенства с модулем

  1. (|x|-1)(2x^2+x-1)\leq 0
  2. \frac{x+1}{|x-1|}+\frac{1-2x}{x-1}\geq 0
  3. \frac{3|x|-11}{x-3}>\frac{3x+14}{6-x}
  4. \displaystyle\frac{|x-1|}{1-\frac{6}{|x-1|}}<-1
  5. \frac{x^2-4x+3}{\sqrt{x-|2x-1|}}\geq 0
  6. \frac{|x-2|+1}{|2x+3|-7}\leq 0
  7. ||x^2-8x+2|-x^2|\geq 2x+2
  8. |x^3+2x^2+2|<|x^3+3x^2+3x-2|
  9. \frac{|x-4|-|x-1|}{|x-3|-|x-2|}<\frac{|x-3|+|x-2|}{|x-4|}
  10. \frac{(x^2+x+1)^2-2|x^3+x^2+x|-3x^2}{10x^2-17x-6}\geq 0

Ответы

  1. [1/2; 1]U{-1}
  2. [0;1)U(1;2]
  3. (-2;2)\cup (2;3)\cup (6; +\infty)
  4. (-5; -1)U(3;7)
  5. (1/3; 1)
  6. (-5; 2)
  7. (-\infty;0]\cup [1;2]\cup [5;+\infty)
  8. (-4;-3/2)\cup (-1;0)\cup (1;+\infty)
  9. (3;4)U(4;7)
  10. (-\infty; -2-\sqrt{3}]\cup (-0,3; -2+\sqrt{3})\cup {1}\cup (2;+\infty)