Question

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

Answer 1

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

Answer 2

the answer has to be in interval notation, so how would that look?

Answer 3

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

Answer 4

thank you I didn't see this post after you posted that!!! you are truly a life saver!!