Odpowiedź :
x(1-3x) < 0
1-3x < 0
-3x < -1 |:(-3)
x > ⅓
x∈(0,⅓)
4x² ≤ 5x
4x²-5x ≤ 0
x(4x-5) ≤ 0
4x-5=0 4x=5 x=1¼
x∈ <0, 1¼>
x < 6x²
6x²-x > 0
x(6x-1) > 0
x = ⅙
x∈ (0,⅙)
(-x+5)(x+2) > 0
-x+5 = 0 x = 5
x+2 = 0 x = -2
x=5 ∨ x=-2
x∈ (-2,5)
(1+x)(3-2x) ≤ 0
1+x = 0 x=-1
3-2x = 0 2x=3 x= 1,5
x=-1 ∨ x=1,5
x∈(-∞,-1>∨<1,5,+∞)
x²<1
x²-1 < 0
(x+1)(x-1) < 0
x=1 ∨ x=-1
x∈(-1,1)
3x²-1>2½ x
3x²-2½x-1>0
Δ=b²-4ac
Δ = (-5/2)²-4*3*(-1) = 25/4+12 = 25/4+48/4 = 73/4
√Δ = √73 / 2
x₁ = 5/2 - √73 / 2 = 5-√73 /2
x₂ = 5+√73 /2
x (-∞, 5-√73 /2 v 5+√73 / 2 , +∞)
x-7 ≥ 5x
-4x-7 ≥ 0
-4 x ≥ 7 /:(-4)
x ≥ -7/4
½ x²-x ≥ 1
½x²-x-1≥0
Δ = (-1)²-4*1/2*(-1) = 1+2 = 3
√Δ = √3
x₁ = 1-√3
x² = 1+√3
(-∞,1-√3> v <1+√3,+∞)
4x²+49≤28x
4x²-28x+49≤0
(2x-7) ≤ 0
2x ≤ 7
x ≤ 3,5