1. ![x(x-2)(9-x)(x+4) \geq 0\\(x - 0)(x - 2)(x - 9)(x + 4) \leq 0 x(x-2)(9-x)(x+4) \geq 0\\(x - 0)(x - 2)(x - 9)(x + 4) \leq 0](https://tex.z-dn.net/?f=x%28x-2%29%289-x%29%28x%2B4%29%20%5Cgeq%200%5C%5C%28x%20-%200%29%28x%20-%202%29%28x%20-%209%29%28x%20%2B%204%29%20%5Cleq%200)
+ -4 - 0 + 2 - 9 +
x ∈ [-4; 0] ∪ [2; 9]
2.![\frac{(x+2)(x+3)}{x-5} \geq 0 \frac{(x+2)(x+3)}{x-5} \geq 0](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B2%29%28x%2B3%29%7D%7Bx-5%7D%20%5Cgeq%200)
- -2 + -3 - 5 +
x ∈ [-2; -3] ∪ [5; ∞)
3.
0\\" alt="\frac{6}{x^2 - 6x} < \frac{1}{x - 6}\\\frac{6 - x}{x(x-6)} < 0\\\frac{(x - 6)}{(x - 0)(x-6)} > 0\\" align="absmiddle" class="latex-formula">
- 0 + 6 +
x ∈ (0;6) ∪ (6; ∞)
4. ![(x-1)^2(2x-1)(x+2) \leq 0\\2(x-1)^2(x- \frac{1}{2})(x + 2) \leq 0 (x-1)^2(2x-1)(x+2) \leq 0\\2(x-1)^2(x- \frac{1}{2})(x + 2) \leq 0](https://tex.z-dn.net/?f=%28x-1%29%5E2%282x-1%29%28x%2B2%29%20%5Cleq%200%5C%5C2%28x-1%29%5E2%28x-%20%5Cfrac%7B1%7D%7B2%7D%29%28x%20%2B%202%29%20%5Cleq%200)
+ -2 - 1/2 + 1 +
x ∈ [-2; 1/2]