Решение
1. б) (x + 2)/(x - 5) < 0
(x + 2)(x - 5) < 0
x + 2 = 0, x = - 2
x - 5 = 0, x = 5
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- 2 5 x
x∈(- 2; 5)
2. - x² + 5x + 14 ≥ 0
x² - 5x - 14 ≤ 0
D = 25 + 4*1*14 = 81
x1 = (5 - 9)/2
x1 = - 2
x2 = (5 + 9)/2
x2 = 7
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- 2 7 x
x∈ (- ∞; - 2] [7; + ∞)
4.
7 - 5x ≤ - 8
x² - 4x < 0
- 5x ≤ - 8 - 7, x ≥ 3, x∈[3; + ∞)
x(x - 4) < 0, x1 = 0; x2 = 4, x ∈(0; 4)
Ответ: x∈[3;4)