x+1/2-x > 2

Setting aside the extent to which this may be a homework problem,
since it's often confusing to express mathematical formulae in
conventional, linear text, perhaps you should clarify if you mean:

"(x+1) dividied by (2-x) is greater than 2" or

"x plus 0.5 minus x is greater than 2"

(I suspect you mean the first one, since the last one would never be true...)

Consider:

  x+1
  --- = 2
  2-x

Then x+1 = 2 (2-x)
So   x+1  = 4 - 2x
So   x+2x = 4-1
So   3x   = 3
So    x   = 1

So, we have a straight line which changes from > to < at x=1

If we try x=1.5

  x+1     1.5+1     2.5
  ---  =  -----  =  --- = 5
  2-x     2-1.5     0.5

And 5 > 2, so larger values of x make the inequality true

So, the original formula is true for all values of x >1

Ratty

x + 1 
-------- >  2
 2 - x

 x + 1 
-------- - 2 > 0
 2 - x

 x + 1 - 4 + 2x 
-------------------- > 0
      2 - x

3x - 3
---------- > 0 
  2 - x

                   - - - - - - -  -   0    + + + + + + 
Sgn(3x-3)         --------------------|----------------------
                                      1
 	                  + + + + + + + + + + +   0 - - - - - -
 Sgn(2-x)         --------------------------------|----------
			               	          2

	             - - - - - - - -  0 + + + + + 0 - - - - - -	
Sgn((3x-3)/(2-x))    -----------------|-----------|---------
		  	              1           2

Answer : 1 < x < 2

----------------------------------------------------

Other way:

(x+1) / (2-x) > 2

If x < 2 then 
x + 1 > 2*(2-x)
x + 1 > 4 - 2x
3x > 3
x > 1       Partial solution 1 < x < 2

If  x > 2 then
x + 1 <  2*(2-x) (the inequation changes because we are multipling by
a negative number)
x + 1 <  4 - 2x
3x < 3
x < 1
 Partial solution is the empty set (x < 1 intersection x > 2 is the empty set)

Then: Answer is 1 < x < 2