Question 922858
One would expect you really mean this:
(x+11)/(x+2)<8, in pure text.

{{{(x+11)/(x+2)<8}}}



The left member would be the expression defining the related function, and the critical points are its roots and any x values which make the function undefined.  Accordingly, the critical values are -11 and -2.


Critical Values of x:   -11 and  -2.


SOLVING THE EQUATION:
{{{(x+11)/(x+2)-8<0}}}
{{{(x+11)/(x+2)-8(x+11)/(x+2)<0}}}
{{{(x+11-8x-88)/(x+2)<0}}}
{{{(-7x-77)/(x+2)<0}}}
{{{(7x+77)/(x+2)>0}}}
Again, examing for critical values of x, they still are -2 and -11.


Three intervals to check.


{{{x<-11}}}:
{{{(7*(-12)+77)/(-12+2)=(-something)/(-someelse)>0}}}  true.
-
{{{-11<x<-2}}}:
{{{(7(-5)+77)/(-5+2)=(something)/(-something)>0}}}  false.
-
{{{x>-2}}}:
{{{(7*0+77)/(0+2)=77/2>0}}}  true.



SOLUTIONS:   ({{{-infinity}}},-11)  OR  (-2, {{{infinity}}})