SOLUTION: Solve the polynomial inequality. Express the solution set in interval notation. -x-6/x+5 is less than or equal to 0.... Please help!!!!!!!!!!!!!!!!!!!!!!!!!!

Algebra ->  Inequalities -> SOLUTION: Solve the polynomial inequality. Express the solution set in interval notation. -x-6/x+5 is less than or equal to 0.... Please help!!!!!!!!!!!!!!!!!!!!!!!!!!      Log On


   

Question 1018975: Solve the polynomial inequality. Express the solution set in interval notation.
-x-6/x+5 is less than or equal to 0....
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean, (-x-6)/(x+5)<=0 ?

%28-x-6%29%2F%28x%2B5%29%3C=0
Identify the critical values for x.
They are what will make numerator or denominator become 0.
-
-x-6=0
x%2B6=0
x=-6
and
x=-5
.
x must not become -5, but this is still a critical x value.
-
Examine the intervals which these critical values form.
x%3C=-6, -6%3C=x%3C-5, -5%3Cx.
Pick any value in each interval and test to see which intervals satisfy the inequality and which do not satisfy the inequality.

Checking Each Interval:
-
%28-%28-6%29-6%29%2F%28-6%2B5%29%3C=0
0%2F-1%3C=0
TRUE
-
%28-%28-5.5%29-6%29%2F%28-5.5%2B5%29%3C=0
%285.5-6%29%2F%28-0.5%29%3C=0
-0.5%2F%28-0.5%29%3C=0
1%3C=0
FALSE
-
%28-%28-4%29-6%29%2F%28-4%2B5%29%3C=0
-2%2F1%3C=0
-2%3C=0
TRUE
-
Interpret those results, and form your solution to the inequality.