SOLUTION: How do I solve (3x+2/x+1) > 4 ?

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Question 1019516: How do I solve (3x+2/x+1) > 4 ?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
All terms and expressions on one side and 0 on the other side.
%283x%2B2%29%2F%28x%2B1%29-4%3E0



Steps to use your fractions-skills.
%283x%2B2%29%2F%28x%2B1%29-4%28x%2B1%29%2F%28x%2B1%29%3E0

%283x%2B2%29%2F%28x%2B1%29-%284x%2B4%29%2F%28x%2B1%29%3E0

%283x%2B2-4x-4%29%2F%28x%2B1%29%3E0

%28-x-2%29%2F%28x%2B1%29%3E0, and now your algebra skills.

%28-1%29%28-x-2%29%2F%28x%2B1%29%3C0

highlight_green%28%28x%2B2%29%2F%28x%2B1%29%3C0%29
Critical values of x are at -2 and -1.
The intervals on the number line to check will be, shown in their interval-notation: ( -infinity,-2), (-2,-1), and (-1, infinity).
Pick any value inside each interval and check how this affects the sign (as "less than zero" or not). 
interval          pick value          expression           LESS THAN ZERO?
(-infin,-2)         -3                 (-1)/(-2)=1/2         NO
(-2,-1)            -3/2              (-1.5+2)/(-1.5+1)       YES
(-1,infin)          0                  2/1=2                 NO

The actually more correct way to check the intervals is to use the ORIGINAL inequality, instead of the transformed version of it as done in the table here. Even so, the solution seems to be highlight%28-2%3Cx%3C-1%29.

Answer by ikleyn(52807) About Me  (Show Source):
You can put this solution on YOUR website!
.
How do I solve (3x+2/x+1) > 4 ?
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It was accurately solved in
http://www.algebra.com/algebra/homework/Rational-functions/Rational-functions.faq.question.1018478.html

See also the lesson Solving inequalities for rational functions with non-zero right side, Problem 3 in this site.