Անհավասարումներ

1)
2x — 4 > 6
2x>10
x>5
x=(5;∞)
2x + 3 ≤ 1
2x≤-2
x≤-1
x=(-∞;-1]
7x — 7 > — 7
7x>-7+7
x>0
x=(0;∞)
10x — 20 > 30
10x>30+20
x>5
x=(5;∞)
25x — 50 ≤ 25
25x≤25+50
x≤3
x=(-∞;3]
4(x — 2) > 2(x + 2)
4x-8>2x+4
4x-2x>4+8
2x>12
x>6
x=(6;∞)
10(x — 4) ≥ 8(x + 2)
10x-40≥8x+16
10x-8x≥16+40
2x≥56
x≥28
x=[28;∞)
2(x — 3) > 4(x + 3)
2x-6>4x+12
2x-4x>12+6
-2x>18
-x>9
x<-9
x=(-∞;-9)
5(x — 2) ≤ 7(x — 3)
5x-10≤7x-21
5x-7x≤-21+10
-2x≤-11
-x≤-5.5
x≥5.5
x=[5.5;∞)

2)
x(x — 5) > 0
x(x-5)=0
x=0
x-5=0, x=5
x=(-∞;0)U(5;∞)
x(2x — 6) > 0
x(2x-6)=0
x=0
2x-6=0, x=3
x=(-∞;0)U(3;∞)
(2x — 4)(3x + 3) > 0
(2x-4)(3x+3)=0
2x-4=0, x=2
3x+3=0, x=-1
x=(-∞;-1)U(2;∞)
(8x + 8)(4x — 4) < 0
(8x+8)(4x-4)=0
8x+8=0, x=-1
4x-4=0, x=1
x=(-1;1)
x(x + 2)(x — 5) ≤ 0
x(x+2)(x-5)=0
x=0
x+2=0, x=-2
x-5=0, x=5
x=(-∞;-2]U[0;5]
(x — 5)(x — 1)(x + 2) > 0
(x-5)(x-1)(x+2)=0
x-5=0, x=5
x-1=0,x=1
x+2=0, x=-2
x=(-2;1)U(5;∞)
(2x — 4)(4x + 4)(5x + 20) > 0
(2x-4)(4x+4)(5x+20)=0
2x-4=0, x=2
4x+4=, x=-1
5x+20=0, x=-4
x=(-4;1)U(2;∞)

3)
(x — 4)/(x + 3) > 0
(x-4)(x+3)=0
x-4=0, x=4
x+3=0, x=-3
x=(-∞;-3)U(4;∞)
(x — 9)/(x + 2) ≥ 0
(x-9)(x+2)=0
x-9=0, x=9
x+2=0, x=-2
x=(-∞;-2]U[9;∞)
(x — 3)/(x + 8) > 0
(x-3)(x+8)=0
x-3=0, x=2
x+8=0, x=-8
x=(-∞;-8)U(2;∞)
(x + 3)/(x — 3) ≤ 0
(x+3)(x-3)=0
x+3=0, x=-3
x=[-3;3]