Question 98512
Before giving out the solution to the problem here is something you should 
know

[x] means the greatest integer value less than or equal to x
so for e.g [1.2] = 1
[-5.6] = -6 
[4]=4

now to the questions 
1. [2x] < 8
   2[x] < 8      (Note [2x] is not = 2[x] but [2x] <= 2[x] so without loss of inequality we can write [2x] as 2[x]) in the above inequality
    [x]< 4
    
  for all x < 4, [x] <4 
hence solution set for the above is x< 4

2. [ p + 2] <6 
   for all p+2 < 6 , [p+2] will be less than 6
   p < 4

3  [z +3 ] >2
   since [z+3] is an integer value [z+3] should be >=3  ( integer greater than 2)

which gives z>=0

4.y-3<2x? (0,0)or(1,5)or(-2,0).
substitue x=0, y=0 
0-3< 2*0
-3 <0 hence it satisfies the equation
Substituting x=1 , y=5 
5-3 < 2*1
2< 2 
It does not satisfy the equation
Substituting x= -2 , y=0
0 - 3 < 2* -2
 -3 < -4 
it does not satisfy the equation

The only point satisfying the equation is (0,0)