1)-(1/2)x > -3
x< -3/-0.5
x < 6
x ∈ (-∞; 6)
2) x^2- 2x+1 ≤ 0
x1 *x2 ≤ 1;
x1 + x2 ≤ 2.
x1 ≤ 1; x2 ≤1
x ∈ (-∞; 1]
3) 3x-x^2 -4 < 0
x1 * x2 < 4;
x1 +x2 < 3.
x1 < 4; x2 < -1
4) 49- x^2 <0 </p>
(7-x)(7+x) < 0
7-x < 0 или 7+x <0</p>
x1 >7 x2 < -7
x ∈ (-∞; -7) U (7; +∞)
5) (3-x)(x+5) > 0
3-x > 0 или x+5 > 0
x1 < 3 x2 > -5
x ∈ (-5; 3)
6) x^2 +2x+1 / x-3 ≥ 0 } * (x-3); ОДЗ: x не равен 3
x^2 +2x+1 ≥ 0
x1 * x2 ≥ 1;
x1 + x2 ≥ -2.
x1 ≥ -1; x2 ≥ -1
x ∈ [-1 ; +∞)
7)x^3 (2x-3)(x-4)^2 (3-x) ≥ 0
1. x^3 ≥0
x1 ≥ 0
2. 2x-3 ≥ 0
2x ≥ 3
x2 ≥ 1,5
3. (x-4)^2 ≥ 0 } * x-4
x-4 ≥ 0
x3 ≥ 4
4. 3-x ≥ 0
x4 ≤ 3
x ∈ (-∞; 0] U [ 1,5 ; 3] U [4]
8) | x+1 | < 2
x+1 < 2 или -(x+1) <2</p>
x1 < 1 -x < 3
x2 > -3
x ∈ (-3; 1)
9) | 7x+ 23|-5 ≥ 0
| 7x+ 23| ≥ 5
7x+23 ≥ 5 или -(7x+23) ≥ 5
7x ≥ -18 или -7x ≥ 28
x1 ≥ -18/7 x2 ≤ -4
x ∈ (-18/7 ; -4)