SOLUTION: (5x+2)/(3x-1)<4

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Question 743489: (5x+2)/(3x-1)<4
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
%285x%2B2%29%2F%283x-1%29%3C4
%285x%2B2%29%2F%283x-1%29-4%3C0
%285x%2B2%29%2F%283x-1%29-4%283x-1%29%2F%283x-1%29%3C0
%28%285x%2B2%29-12x%2B4%29%2F%283x-1%29%3C0
%286-7x%29%2F%283x-1%29

Next we test on the intervals that our boundary values generated:
First interval:
-infinity%3Cx%3C1%2F3
Suppose x=0
then our inequality gives us
-2%3C4 <---TRUE!

Second interval:
1%2F3%3Cx%3C6%2F7

Suppose x=0.5
then our inequality gives us
9%3C4 <---False!
Third interval:
6%2F7%3Cx%3Cinfinity

Suppose x=1
then our inequality gives us
7%2F2%3C4 <---TRUE!

solution:
-infinity%3Cx%3C1%2F3 union 6%2F7%3Cx%3Cinfinity