How do you solve inequalities?

Question

What are the values for x for which (x-2)(x+5) >0 ?

Answer 1

(x-2)(x+5) >0
bcoz (x-2)(x+5) should alwayz be +ve so
x>2 orx<-5

Answer 2

x < -5 & x > 2

What you need to do first is find your critical points.

Set x-2=0 and x+5=0, and solve for x. So your critical points are 2 and -5. Choose a value less than -5, and see if it will make your inequality true. So, if you pick -7, you get (-7-2)(-7+5)>0, which is true because when you multiply two negatives you get a positive. If you choose a value between -5 and 2 the above inequality will not be true. If you choose a value > 2 the inequality will be true.

Answer 3

in dealing with the problem

(x-2)(x+5)>0

first, solve for the critical values...

x - 2 = 0
x = 2

x +5 = 0
x = -5

therefore, the critical values are 2 and -5

then, this is the shortcut..
the one with the larger value retains the inequality sign while the smaller value changes the inequality sign...

so the answer will be

x > 2 or x < -5

hope it helps

Answer 4

The correct answer is the one chasrmck gave you.
The explanation is:
(x-2)(x+5)>0
the expression on the left will be positive if and only if:
- (x-2)>0 and (x+5)>0 (+*+=+)
OR
- (x-2)<0 and (x+5)<0 (-*-=-)
from here you get chasrmck's answer.
I hope I was clear enough.

Answer 5

x>2 and x>-5 requires x>2
or
x<2 and x<-5 requires x<-5

So x can be any number less than -5 or greater than 2

Answer 6

(x-2)(x+5) >0

so, either (x-2) > 0 i.e. x > 2
or, (x+5) > 0 i.e. x > -5

so combining both we have x > 2 (because x > 2 automatically implies x > -5)

Answer 7

3 or three.