Решите неравенство:

|х-14| меньше, либо равно 8+2 х

|х+5| > 5 х-7

|х^2+х-5| > 3 х

1) |х-14|≤ 8+2 х

a) x-14 ≤ 8+2x

-x≤22

x≥-22

b) - x+14≤8+2x

-3x≤-6

x≥2

x ∈ [2; + ∞)

2) |х+5| > 5 х-7

a) x+5 > 5x - 7

-4x > - 12

x < 3

b) - x-5 > 5x-7

-6x > - 2

x < 1/3

x∈ (-∞; 1/3)

3) |х^2+х-5| > 3 х

a) x² + x - 5 > 3x

x² - 2x - 5 > 0

x² - 2x - 5 = 0

D = 4 + 20 = 24

x₁ = (2+2√6) 2 = 1 + √6

x₂ = 1 - √6

x ∈ (-∞; 1 - √6) U (1 + √6; + ∞)

b) - x² - x + 5 > 3x

-x² - 4x + 5 > 0

x² + 4x - 5 > 0

x² + 4x - 5 = 0

x₁ = 1

x₂ = - 5

x ∈ (-∞; - 5) U (1; + ∞)

x ∈ (1 - √6; 1)