algebra
posted by sarah on .
Solve the following inequality and write answer using interval notation. Please show all of your work.
2x5/3x^4x^3+275x125>=0

Your casual use of parentheses makes me assume you mean
(2x5)/(3x^4  x^3 + 275x  125) >= 0
let's try to factor the denominator. We get not much help.
You sure you don't mean
3x^4  x^3 + 375x  125?
That would be
x^3 (3x1) + 125(3x1)
(x^3+125)(3x1)
(x+5)(x^2  25x + 25)(3x1)
Anyway, working with your original function, the denominator is positive when x < 4.54 or x > 0.45
The numerator is positive when x > 2.5
If you plot the points 4.54, 0.45, 2.5 on the number line, you will see
on (oo,4.54) we have +/ so y < 0
on (4.54,0.45) we have / so y > 0
on (0.45,2.5) we have +/ so y < 0
on (2.5,oo) we have +/+ so y > 0
y>0 on [4.54,0.45] U [2.5,oo)