Posted by **MYA** on Wednesday, September 5, 2012 at 8:31pm.

solve the following inequality

x^2(8+x)(x-5)/ (x+5)(x-2)> or equal too 0

this looks like a fraction

please show work

- college alg -
**Reiny**, Wednesday, September 5, 2012 at 9:01pm
critical values:

x=0 , x=-8, x=5, x=-5 and x=2

So want to see where the graph of

y = x^2(8+x)(x-5)/ ((x+5)(x-2)) lies above or on the x-axis

investigate the following domains

1. x < -8

2. x between -8 and -5

3. x between -5 and 0

4. x between 0 and 2

5. x between 2 and 5

6. x > 5

You don't actually have to work out the calculations, all you care about is whether the answer is + or -

I will do 5.

a number between 2 and 5, I pick x = 4

then

(+)(+)(-)/((+)(+)) ≥ 0 ?? , no,

so x between 2 and 5 is not a solution

You can do the others the same way

I also graphed y = x^2(8+x)(x-5)/((x+5)(x-2))

http://www.wolframalpha.com/input/?i=y+%3D+x%5E2%288%2Bx%29%28x-5%29%2F%28%28x%2B5%29%28x-2%29%29

which confirmed that

x<-8 OR -5 < x < 2 OR x > 5

- college alg -
**MYA**, Wednesday, September 5, 2012 at 9:11pm
the answer has to be in interval notation, so how would that look?

- college alg -
**Reiny**, Wednesday, September 5, 2012 at 10:14pm
I am not a big fan of "interval notation"

Back in the dark ages when I taught we used the above notation, which is much more specific

Here is a page that shows "interval notation", look about half way down the page.

It should be quite easy to convert my answer to what you need.

http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm

- college alg -
**For Reiny**, Wednesday, September 5, 2012 at 11:11pm
thank you I didn't see this post after you posted that!!! you are truly a life saver!!

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