SOLUTION: how do I solve this inequality? 8x-12 > 8/x

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Question 890100: how do I solve this inequality?
8x-12 > 8/x
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!


Do NOT multiply each side by x.



Bring the first two terms to higher-terms according to denominator x.


There, you want to use the NUMERATOR to see how it is related to zero; the denominator will not really be relevant, except that the solution for x must EXCLUDE x=0.

The important critical points are at x being the zeros of the numerator.






The inequality will be satisfied for or for ----
The possibility of x=0 will no longer be necessary to consider since it is not within the domain for this inequality.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
how do I solve this inequality?
8x-12 > 8/x


........

 ------ Multiplying both sides be LCD, x







 

2x + 1 = 0          OR          x - 2 = 0 ------- Converting inequality to equality

2x = - 1            OR          x = 0 + 2

              OR          x = 2

Critical points are , , since , and .

Therefore the four intervals to check are: , , , and .

Intervals that satisfy INEQUALITY:  and  

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