§ 5: 5.13

5.13 Розв’яжіть нерівність:

1) 1x+2 ≤ 1, 1-(x+2)x+2 ≤ 0, 1-x-2x+2 ≤ 0, -x-1x+2 ≤ 0, x+1x+2 ≥ 0,

x ∈ (–∞; –2) ∪ [–1; +∞);]

2) xx+1 ≥ 2, x-2(x+1)x+1 ≥ 0, x-2x-2x+1 ≥ 0, -x-2x+1 ≥ 0, x+2x+1 ≤ 0,

x ∈ [–2; –1);

3) 5x+84-x < 2, 5x+8 -2(4-x)4-x < 0, 5x+8 -8 + 2x4-x < 0, 7x4-x < 0,

x ∈ (–∞; –0) ∪ (4; +∞);

4) 2x+3 ≥ 1x-1, 2x-1- (x+3)x+3(x-1) ≥ 0, 2x-2-x-3x+3(x-1) ≥ 0, x-5x+3(x-1) ≥ 0,

x ∈ (–3; 1) ∪ [5; +∞).