- #1

deryk

- 10

- 0

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? I am not sure what to do now with the product being bigger or smaller than 0. Thanks for your time.

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- Thread starter deryk
- Start date

- #1

deryk

- 10

- 0

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? I am not sure what to do now with the product being bigger or smaller than 0. Thanks for your time.

- #2

lurflurf

Homework Helper

- 2,458

- 156

Right so far.deryk said:

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? I am not sure what to do now with the product being bigger or smaller than 0. Thanks for your time.

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:

- #3

deryk

- 10

- 0

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

- #4

lurflurf

Homework Helper

- 2,458

- 156

you missed -2<x<-1/2deryk said:thanks lurf lurf .I got x>2. Does anyone know if that's right?

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

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