Question 1060412
(3x+1)/(x+4)>=1


{{{(3x+1)/(x+4)>=1}}}


{{{(3x+1)/(x+4)-(x+4)/(x+4)>=0}}}


{{{(3x+1-x-4)/(x+4)>=0}}}


{{{(2x-3)/(x+4)>=0}}}
Critical x values are at {{{3/2}}} 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.


<pre>
                           CHOOSE A VALUE x       CHECK SIGNS      RESULT

{{{-infinity<x<-4}}}                 -5                  (-)/(-)=(+)      TRUE

{{{-4<x<=3/2}}}                    0                (-)/(+)=(-)        FALSE

{{{3/2<=x<infinity}}}                     3                 (+)/(+)=(+)       TRUE
</pre>

SOLUTION:  {{{system(x<-4, OR, x>=3/2)}}}