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x^3-144x<0

 Oct 15, 2015
 #1
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x^3-144x<0   .....let's factor the left side as

 

x(x -144) < 0  =  x( x + 12) (x - 12) < 0

 

The solution comes from one, or more, of these intervals :

 

(-inf, -12) (-12, 0) (0, 12) (12, inf)

 

If we pick the test points,  - 13, -3, 3, and 13   and put them in the factored equation, -3 and 13 make the inequality true, but -13 and 3 make it false

 

So.....the solution intervals are (-12, 0) and (12, inf)

 

Here's a graph that will show this is true :   https://www.desmos.com/calculator/uc5lu7mmsj

 

 

 

cool cool cool

 Oct 15, 2015
edited by CPhill  Oct 15, 2015

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