SOLUTION: Solve (3x+1)/(x+4) > or = 1

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Question 1060412: Solve (3x+1)/(x+4) > or = 1
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
(3x+1)/(x+4)>=1

%283x%2B1%29%2F%28x%2B4%29%3E=1

%283x%2B1%29%2F%28x%2B4%29-%28x%2B4%29%2F%28x%2B4%29%3E=0

%283x%2B1-x-4%29%2F%28x%2B4%29%3E=0

%282x-3%29%2F%28x%2B4%29%3E=0
Critical x values are at 3%2F2 and -4. The first of those because of the numerator, the second of those because of the denominator.
The critical x values tell you the intervals on the x number line to check the truth of falsity of the inequality. 

                           CHOOSE A VALUE x       CHECK SIGNS      RESULT

-infinity%3Cx%3C-4                 -5                  (-)/(-)=(+)      TRUE

-4%3Cx%3C=3%2F2                    0                (-)/(+)=(-)        FALSE

3%2F2%3C=x%3Cinfinity                     3                 (+)/(+)=(+)       TRUE

SOLUTION: system%28x%3C-4%2C+OR%2C+x%3E=3%2F2%29