Question 937712
Critical values of x are at -(1/3) and 2.


{{{(2-x)/(3x+1)<=0}}}


Check the sign of the expression in the three intervals  (-infinity, -1/3], [-1/3, 2], [2, infinity).



Interval______________sign comb.______sign
{{{x<-1/3}}}____________(+)/(-)___________(-)
{{{-1/3<=x<=2}}}________(+)/(+)_____________(+)
{{{2<=x}}}____________(-)/(-)___________(+)


Solution:  ( -infinity, -1/3 ]
because the sign being negative for the rational expression means that the expression is less than  (or in this case, equal to ) zero.