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Solve the inequality x^3 + 4x > 5x^2 + 4x.

 Aug 12, 2021
 #1
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Subtract  4x  from both sides

 

x^3  >  5x^2          rearrange  as

 

x^3  - 5x^2  >  0        factor  as

 

x^2  ( x - 5) >  0

 

Set  as  an equality

 

x^2 ( x - 5)  =  0

 

The  possible  solution intervals  are   x  =     ( -inf , 0)    or  ( 0, 5)  or   ( 5 , inf)

 

If  we let x < 5 , the  first two intervals do not solve the original inequality

 

So......the  solution is   ( 5, inf)

 

cool cool cool

 Aug 12, 2021

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