Question 1209292
<pre>
{{{red((3 - z)/(z + 1)) >= green(2 + 1/(z - 7))}}}

Draw the graph of the left side and the right side:

{{{drawing(400,400,-10,10,-10,10,
blue(line(-1,-20,-1,20),line(7,-20,7,20)),
graph(400,400,-10,10,-10,10,(3-x)/(x+1),2 + 1/(x - 7)))}}}

The exact solutions are ugly.

I found the approximate solutions of their points of
intersection with a TI-84. They are 

0.4043040632... and 6.595695937...

There are asymptotes at -1 and 7.
The red curve is the graph of the left side.
The green curve is the graph of the right side.
The blue vertical lines are the asymptotes.

The red curve is above or intersecting the green curve
between the asymptote at -1 and the smaller solution.
So that part is the interval:

(-1, 0.4043040632...]

The red curve is above or intersecting the green curve
again between the larger solution and the asymptote at 7
So that part is the interval:
   
[6.595695937..., 7)

So the solution is 

(-1, 0.4043040632...] U [6.595695937..., 7)

Edwin</pre>