# Inequality

• April 20th 2012, 03:47 AM
iFuuZe
Inequality

x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to
• April 20th 2012, 03:49 AM
Prove It
Re: Inequality
Quote:

Originally Posted by iFuuZe

x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to

You need to use brackets where they're needed so we can understand what the inequation actually is.

Is it \displaystyle \begin{align*} \frac{x^3 + 5x^2 + 2x - 8}{x^3 - 7x^2 + 7x + 15} \leq 0 \end{align*}?
• April 20th 2012, 04:04 AM
princeps
Re: Inequality
Quote:

Originally Posted by iFuuZe

x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to

Inequality is equivalent to the :

$\frac{(x-1)(x+4)(x+2)}{(x-5)(x-3)(x+1)} \leq 0$
• April 20th 2012, 04:09 AM
iFuuZe
Re: Inequality
yep so you factorice the top and bottom now what we do procede....
• April 20th 2012, 04:12 AM
Prove It
Re: Inequality
Quote:

Originally Posted by iFuuZe
yep so you factorice the top and bottom now what we do procede....

A function will only ever stop being negative at the x intercepts, so evaluate where they are, then test some points between each of them to determine which of the regions give negative values for the function :)
• April 20th 2012, 04:14 AM
princeps
Re: Inequality
• April 20th 2012, 04:18 AM
a tutor
Re: Inequality
Quote:

Originally Posted by Prove It
A function will only ever stop being negative at the x intercepts...

or at a discontinuity. (Nerd)
• April 20th 2012, 04:41 AM
Prove It
Re: Inequality
Quote:

Originally Posted by a tutor
or at a discontinuity. (Nerd)

Let's assume we've already established that \displaystyle \begin{align*} x \neq -1, 3, 5 \end{align*} :P
• April 20th 2012, 04:48 AM
a tutor
Re: Inequality
Quote:

Originally Posted by Prove It
Let's assume we've already established that \displaystyle \begin{align*} x \neq -1, 3, 5 \end{align*} :P

Of course.

I'm just pointing out that you can get a sign change at a discontinuity too.
• April 20th 2012, 04:56 AM
iFuuZe
Re: Inequality
guys i dont understand, its better if i visualise a worked example if any can do that it would fantastic
• April 20th 2012, 05:25 AM
a tutor
Re: Inequality
Sign changes occur whenever the sign of one factor changes.

This will happen at x= -4,-2,-1,1,3 and 5.

So check x<-4. Here all factors <0 so the expression is positive.

x<-4 positive
-4<x<-2 negative
-2<x<-1 positive
-1<x<1 negative
1<x<3 positive
3<x<5 negative
x>5 positive