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. \((-\infty; -2-\sqrt{3}]\cup (-0,3; -2+\sqrt{3})\cup {1}\cup (2;+\infty)\)