SOLUTION: I have a few I can't find examples for in my book... 1. x^4 < x^2 2. 2/x+8 > 3/x-9 3. x^3-5x^2-5x+25>0

Algebra ->  Inequalities -> SOLUTION: I have a few I can't find examples for in my book... 1. x^4 < x^2 2. 2/x+8 > 3/x-9 3. x^3-5x^2-5x+25>0      Log On


   

Question 422394: I have a few I can't find examples for in my book...
1. x^4 < x^2
2. 2/x+8 > 3/x-9
3. x^3-5x^2-5x+25>0
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. x^4 < x^2
Divide both sides by x^2, results
x^2 < 1
:
2. 2%2F%28x%2B8%29+%3E+3%2F%28x-9%29
Cross multiply
2(x-9) > 3(x-9)
2x - 18 > 3x - 27
3x - 3x > - 27 + 18
-x > - 9
x has to be positive, mult both sides by -1, this reverses the inequality sign
x < 9
:
3. x^3 - 5x^2 - 5x + 25 > 0
graph this
+graph%28+300%2C+200%2C+-5%2C+10%2C+-20%2C+30%2C+x%5E3+-+5x%5E2+-+5x+%2B+25%29+
you can see x > 0 -2.2 to +2.2; when x > 5