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

Thank you!

 Mar 15, 2020
edited by Guest  Mar 15, 2020
 #1
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Divide by x: x^2 + 4 > 5x

Move terms: x^2 - 5x + 4 > 0

Factor: (x - 1)(x - 4) > 0

Answer: (-inf,1) U (4,inf)

 Mar 15, 2020
 #2
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Thank you so much!

smallbrain  Mar 15, 2020
 #3
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Here is another way to put it:

 

We find the GCF of all of the terms, which is x. That will get us x^2+4>5x

This can be set into a quadratic (ax^2+bx+c). 

In this case, the quadratic will be x^2-5x+4.

 

We will then factor the quadratic, which will get us (x - 1)(x - 4) > 0

 

The possible values of x will be x=1 and x=4.

 

If we write this in interval notation, it will be (-infinity, 1) U (4, infinity) 

 Mar 21, 2020

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