Question 913462
Make all numbers onto one side of the order relation.


{{{7/(x+1)-7>0}}}


{{{1/(x+1)-1>0}}}


{{{(1-(x+1))/(x+1)>0}}}


{{{-x/(x+1)>0}}}
The critical values are x at 0 and -1.  These form three intervals for the real x number line.


(-infinity, -1)
Pick any value, example, -3.
{{{-(-3)/(-3+1)}}}
{{{3/(-2)}}}
{{{-3/2>0}}}
FALSE.


(-1, 0)
Pick some value, -1/2.
{{{-(-1/2)/(-1/2+1)}}}
{{{(1/2)/(1/2)}}}
{{{1>0}}}
TRUE.


(0, infinity)
Pick a value greater than 0, like 1.
{{{-1/(1+1)}}}
{{{-1/2>0}}}
FALSE.


One more thing:  The original inequality seems to have no restriction for x at 0; so maybe x=0 might work.  Check this.
{{{7/(0+1)>7}}}   ?
{{{7/1>7}}}
{{{7>7}}}
FALSE!


RESULT, ANSWER:  {{{highlight(highlight(-1<x<0))}}}