What are the elements of the set whose properties is |x-2|=

l x-2 l =< 3

Then we
have two cases:

(x-2) =< 3     OR   -(x-2) =
< 3

Let us solve each
case:

case (1):

x-2 =<
3

add 2 to both
sides:

==> x =<
5

==> since x is an integer,
Then:

x= { -inf, ....,
-1,0,1,2,3,4,5}.........(1)

Case(2):

-(x-2)
=< 3

==> -x + 2 =<
3

subtract 2 :

==> -x
=< 1

Now multiply by
-1:

==> x >=
-1

==> x= { -1, 0, 1, ....,
inf}.........(2)

Now the solution
is:

x = (1) and
(2)

==> x = { -1, 0, 1, 2, 3, 4,
5}