1) (x⁴ - 27x)(x² - 4x - 5) < 0
x(x³ - 27)(x - 5)(x + 1) < 0
x(x - 3)(x² + 3x + 9)(x - 5)(x + 1) < 0
x² + 3x + 9 > 0 при любых значениях x . Разделим обе части на это выражение :
x(x - 3)(x - 5)(x + 1) < 0
+ - + - +
________₀_________₀__________₀_________₀________
- 1 0 3 5
x ∈ (- 1 ; 0) ∪ (3 ; 5)
![2)\frac{7x+4}{3-2x}\geq2\\\\\frac{7x+4}{3-2x}-2\geq0\\\\\frac{7x+4-6+4x}{3-2x}\geq0\\\\\frac{11x-2}{3-2x}\geq0\\\\11*(-2)(x-\frac{2}{11})(x-1,5)\geq0\\\\(x-\frac{2}{11})(x-1,5)\leq0 2)\frac{7x+4}{3-2x}\geq2\\\\\frac{7x+4}{3-2x}-2\geq0\\\\\frac{7x+4-6+4x}{3-2x}\geq0\\\\\frac{11x-2}{3-2x}\geq0\\\\11*(-2)(x-\frac{2}{11})(x-1,5)\geq0\\\\(x-\frac{2}{11})(x-1,5)\leq0](https://tex.z-dn.net/?f=2%29%5Cfrac%7B7x%2B4%7D%7B3-2x%7D%5Cgeq2%5C%5C%5C%5C%5Cfrac%7B7x%2B4%7D%7B3-2x%7D-2%5Cgeq0%5C%5C%5C%5C%5Cfrac%7B7x%2B4-6%2B4x%7D%7B3-2x%7D%5Cgeq0%5C%5C%5C%5C%5Cfrac%7B11x-2%7D%7B3-2x%7D%5Cgeq0%5C%5C%5C%5C11%2A%28-2%29%28x-%5Cfrac%7B2%7D%7B11%7D%29%28x-1%2C5%29%5Cgeq0%5C%5C%5C%5C%28x-%5Cfrac%7B2%7D%7B11%7D%29%28x-1%2C5%29%5Cleq0)
+ - +
_________[2/11]__________(1,5)___________
x ∈ [2/11 ; 1,5)