Question

Resolva as inequações determine o seguinte conjunto:

1
(a) (x-4) (x+2)>0
(b) (x+5) (x-2)>0
(c) (x+6) (x+4)<0

2
(a) X+2>0
-x-4>0
(b) 2x+8>0
3x+9>0
(c) 2x+5>x
3x+6>0
3
(a) 3x+6<0
x+3
(b) 3x+3
-x-3
(c) x+3>0
-x-3
(d) 2x+8<0
x+2

Answer 1

1.-)
a)(x-4)(x+2)>0
x^2 +2x - 4x - 8 > 0
x^2 - 2x - 8 > 0
(x-4)(x+2)>0
x1 - 4 > 0》x1 = 4
x2 + 2 > 0》x2 = - 2

b) (x+5)(x-2)>0
x^2 - 2x + 5x - 10 > 0
x^2 - 3x - 10 > 0
(x-5)(x+2)>0
x1 - 5 > 0》x1 = 5
x2 + 2 > 0》x2 = - 2

c) (x+6)(x+4)<0
x^2 + 4x +6x + 24 < 0
x^2 + 10x + 24 < 0
(x+6)(x+4)<0
x1 + 6 < 0》x1 = - 6
x2 + 4 < 0》x2 = - 4

2.-)
a) x+2>0
-x-4>0
-------------
x > -2
-x > 4 (-1)》x > -4

b)2x+8>0
3x+9>0
--------------
2x>-8》x>-8/2》x>-4
3x>-9》x>-9/3》x>-3

c) 2x+5>x
3x+6>0
--------------
2x-x>-5》x > -5
3x>-6》x > -6/3》x > -2

3.-)
a) 3x+6<0
x+3<0
--------------
3x<-6》x<-6/3》x<-2
x<-3

b) 3x+3=0
-x-3=0
---;----------;
3x=-3》x=-3/3》x=-1
-x=3 (-1)》x=-3

c) x+3>0
-x-3>0
-------------
x>-3
-x>3(-1)》x=-3

d) 2x+8<0
x+2<0
---;;---------;-
2x<-8》x<-8/2》x<-4
x<-2