Find the range of x if 8x<3x^2.

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- Jan 31st 2010, 03:56 AMmastermin346Quadratic Inequalities
Find the range of x if 8x<3x^2.

- Jan 31st 2010, 04:05 AMHenryt999Maybe this will help
$\displaystyle 8x <3x^2$

$\displaystyle 8x-3x^2<0$

$\displaystyle x(8-3x)<0$

For the inequality to be negative either x<0 and 8-3x>0 or x>0 and 8-3x<0

Check when the factors changes signs. x is easy, its when it is smaller then zero.

Like this

Factor/ -8/3 0 8/3

x: - 0 +

8-3x:

this one you have to fill in yourself

Then it is easy to see when both factors have opposite signs..