1) x²+3x-4 < 0
x²+4x-x-4 < 0
x(x+4)-(x+4) < 0
(x-1)(x+4) < 0
____+____-4____-____1____+____
x ∈ (-4; 1)
2) 4x²-8x ≥ 0
4x(x-2) ≥ 0
x(x-2) ≥ 0
____+____0____-____2____+____
x ∈ (-∞; 0] ∪ [2; ∞)
3) x²-6x+10 > 0
D = -1 < 0 =>
xв = -b/2a = 6/2 = 3
yв = 9 - 18 + 10 = 1 =>
x ∈ (-∞; ∞)
4) x²-10x+25 ≤ 0
(x-5)² ≤ 0
____+____5____+____
x ∈ {5}
5) (x+2)(x-3) > 0
____+____-2____-____3____+____
x ∈ (-∞; -2) ∪ (3; ∞)
6) (4x-1)(x+2) ≥ 9
4x²+8x-x-2-9 ≥ 0
4x²+7x-11 ≥ 0
(x+2.75)(x-1) ≥ 0
____+____-2.75____-____1____+____
x ∈ (-∞; -2.75] ∪ [1; ∞)