SOLUTION: Find the solution set to this inequality {{{6x/(7x-2)}}} > {{{2/(x+1)}}}

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Question 596805: Find the solution set to this inequality
6x%2F%287x-2%29 > 2%2F%28x%2B1%29
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!

 6x%2F%287x-2%29 > 2%2F%28x%2B1%29

Get 0 on the right side:

 6x%2F%287x-2%29 - 2%2F%28x%2B1%29 > 0

Get an LCD on the left of (7x-2)(x+1):

 6x%2F%287x-2%29%22%22%2A%22%22%28x%2B1%29%2F%28x%2B1%29- 2%2F%28x%2B1%29%22%22%2A%22%22%287x-2%29%2F%287x-2%29 > 0

 %286x%2A%28x%2B1%29%29%2F%28%287x-2%29%28x%2B1%29%29 - %282%287x-2%29%29%2F%28%28x%2B1%29%287x-2%29%29 > 0

 %286x%2A%28x%2B1%29-2%2A%287x-2%29%29%2F%28%287x-2%29%28x%2B1%29%29 > 0

 %286x%5E2%2B6x-14x%2B4%29%2F%28%287x-2%29%28x%2B1%29%29 > 0

 %286x%5E2-8x%2B4%29%2F%28%28x-2%29%28x%2B1%29%29 > 0

Factor 2 out of the top:

 %282%283x%5E2-4x%2B2%29%29%2F%28%287x-2%29%28x%2B1%29%29 > 0

Divide both sides by 2

%283x%5E2-4x%2B2%29%2F%28%287x-2%29%28x%2B1%29%29 > 0

The numerator has no real zeros.
Find real zeros of the denominator 

7x-2 = 0,    x+1 = 0
   x = 2%2F7,      x = -1

-----o--------o--------
    -1        2%2F7

Possible 
intervals 
   for 
solutions:   | (-∞,-1) | (-1,2%2F7) | (2%2F7,∞)
-----------------------------------------
test value   |   -2    |    0   |   1   
-----------------------------------------
sign of f(x) |    +    |    -   |   +
-----------------------------------------     
f(x) > 0     |   YES   |   NO   | YES

Solution:   (-∞,-1) ⋃ (2%2F7,∞)    

Edwin