1) 2x+5,4x-1,8≥0 2) x+4≤ - 3/x 3) x^2+5x+18/x-4 ≥ -2 4) (x^2-6x+8) (x-2)^3/(x+4)^5 (5-x)^3≥0 5) 1/x-1 + 1/x+3 ≤ 2/x+4

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вопрос

1) To solve 2x + 5, 4x - 1, 8 ≥ 0, first simplify the inequality:
2x + 5 ≥ -4x + 1
Rearrange:
6x ≥ -4
x ≥ -2/3

2) To solve x + 4 ≤ -3/x, first simplify the inequality:
x + 4 ≤ -3/x
Rearrange:
x^2 + 4x + 3 ≥ 0
Factor:
(x + 3)(x + 1) ≥ 0
x ≤ -3 or x ≤ -1

3) To solve x^2 + 5x + 18/x - 4 ≥ -2, first simplify the inequality:
x^2 + 5x + 18/x - 4 + 2 ≥ 0
x^2 + 5x + 18/x - 2 ≥ 0
(x + 3)(x + 6)/x - 2 ≥ 0
(x + 3)(x + 6) ≥ 0 for x ≠ 2

4) To solve (x^2 - 6x + 8)(x - 2)^3/(x + 4)^5(5 - x)^3 ≥ 0, analyze each part of the inequality separately and consider all cases

5) To solve 1/x - 1 + 1/x + 3 ≤ 2/x + 4, first simplify the inequality:
1/x - 1 + 1/x + 3 - 2/x - 4 ≤ 0
1/x + 1/x - 2/x - 2 ≤ 0
1/x - 2/x - 2 ≤ 0
-1/x - 2 ≤ 0
-1/x ≤ 2
x ≥ -1/2