Question 1018975
Do you mean,  (-x-6)/(x+5)<=0 ?


{{{(-x-6)/(x+5)<=0}}}
Identify the critical values for x.
They are what will make numerator or denominator become 0.
-
{{{-x-6=0}}}
{{{x+6=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<=-6}}}, {{{-6<=x<-5}}}, {{{-5<x}}}.
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:
-
{{{(-(-6)-6)/(-6+5)<=0}}}
{{{0/-1<=0}}}
TRUE
-
{{{(-(-5.5)-6)/(-5.5+5)<=0}}}
{{{(5.5-6)/(-0.5)<=0}}}
{{{-0.5/(-0.5)<=0}}}
{{{1<=0}}}
FALSE
-
{{{(-(-4)-6)/(-4+5)<=0}}}
{{{-2/1<=0}}}
{{{-2<=0}}}
TRUE
-
Interpret those results, and form your solution to the inequality.