# Solving inequalties

1. Aug 5, 2005

### deryk

Im trying to solve (4x-4)/(x+2)< 2x-3

I get it down to 0<(2x+1)(x-2) if x+2>0

0>(2x+1)(x-2) if x+2<0

Are these right so far? Im not sure what to do now with the product being bigger or smaller than 0. Thanks for your time.

2. Aug 5, 2005

### lurflurf

Right so far.
You have products
the sign of a product depends on the sighns of the factors
ab>0
means
a>0 and b>0
or
a>0 and b<0
ab<0
means
a>0 and b<0
or
a<0 and b>0

another way to think about it is (2x+1)(x-2) is a continuos function
find out where the zeros are
call them a and b with a<b
consider the intervals (since -2 is also an important number)
x<-2
-2<x<a
a<x<b
b<x
all the points in one of these intervals satisfy the inequality or none do
so checking one point in each intervals tells you if the whole interval satifies the inequality

Last edited: Aug 5, 2005
3. Aug 5, 2005

### deryk

thanks lurf lurf .I got x>2. Does anyone know if that's right?

4. Aug 5, 2005

### lurflurf

you missed -2<x<-1/2
consider for example x=-1
(4x-4)/(x+2)< 2x-3
(4(-1)-4)/((-1)+2)< 2(-1)-3
(-4-4)/1<-2-3
-8<-5