# What are the elements of the set whose properties is |x-2|=<3 ?The elements are integer numbers.

hala718 | Certified Educator

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

==> 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}

giorgiana1976 | Student

From enunciation, we find out that the elements of the set, have to respect the constraint that they are integer numbers which have the property |x-2|=<3

We'll re-write the constraint |x-2|=<3:

-3=<x-2=<3

We'll solve the left side of the inequality:

-3=<x-2

0=<x-2+3

0=<x+1

We'll subtract 1 both sides:

-1=<x

Now, we'll solve the right side:

x-2=<3

We'll add 2 both sides, to isolate x:

x=<5

So, -1=<x=<5

The integer elements of the set are:{-1 ; 0 ; 1 ; 2 ; 3 ; 4 ; 5}.