SOLUTION: Solve the inequality (2-x)/(3x+1) less than or equal to 0 giving answer in interval notation

Algebra ->  Inequalities -> SOLUTION: Solve the inequality (2-x)/(3x+1) less than or equal to 0 giving answer in interval notation      Log On


   

Question 937712: Solve the inequality
(2-x)/(3x+1) less than or equal to 0 giving answer in interval notation
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Critical values of x are at -(1/3) and 2.

%282-x%29%2F%283x%2B1%29%3C=0

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


Interval______________sign comb.______sign
x%3C-1%2F3____________(+)/(-)___________(-)
-1%2F3%3C=x%3C=2________(+)/(+)_____________(+)
2%3C=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.