What are possible values of m if l2m+3l

l 2m +3 l <12

We need to
find the values of m such that m belongs to Z.

By definition we will
rewrite:

==> -12 < 2m+3 <
12

We will subtract 3 from both
sides.

==> -15 < 2m <
9

Now we will divide by
2.

==> -15/2 < m <
9/2

==> -7.5 < m <
4.5

Since m is an integer, then we will find all
integers between -7.5 and
4.5

==> m = { -7, -6, -5, -4,
-3, -2, -1, 0, 1, 2, 3, 4}