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; ∞)