Saturday, May 4, 2013

Solve the inequality

%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

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