Algebra Problem

Question

(x+2)(x-1)(x-8)>0

Answer 1

Another way is the following

 (x+2)(x-1)(x-8)>0 ⇒

The re are following possibilities

 

1)    x+2>0, x-1>0,  x-8>0

 

or

2)    x+2<0, x-1<0, x-8>0

 

or  

 3)    x+2>0, x-1<0, x-8<0

 

or

4)  x+2<0, x-1>0,  x-8<0

 

 Now look at each case separately

1) x>-2, x<1, x>8 ⇔ x>8

2)  x<-2, x<1, x>8 ⇔ x ∈∅

3)  x>-2, x<1, x<8  ⇔ -2<x<1

 

4) x<-2, x>1, x<8  ⇔ x ∈∅

So the answer is -2<x<1 and x>8 or as stated be Michael J. (-2, 1)∪(8, ∞).

 

 

Answer 2

First find the zeros of the inequality.

 

x = -2     ,        x = 1       ,     x = 8

 

 

If we look at the graph of the cubic function, we can see where the curve is above the x-axis.  This happens in the interval

 

(-2, 1)∞(8, ∞)