college alg
posted by MYA on .
solve the following inequality
x^2(8+x)(x5)/ (x+5)(x2)> or equal too 0
this looks like a fraction
please show work

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)(x5)/ ((x+5)(x2)) lies above or on the xaxis
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)(x5)/((x+5)(x2))
http://www.wolframalpha.com/input/?i=y+%3D+x%5E2%288%2Bx%29%28x5%29%2F%28%28x%2B5%29%28x2%29%29
which confirmed that
x<8 OR 5 < x < 2 OR x > 5 
the answer has to be in interval notation, so how would that look?

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