What are the values of M if l 2m -5 l

l 2m - 5 l < 12

First
we will solve the inequality the same way we solve the
equations.

We have two
cases.

Case(1):

(2m - 5)
< 12

==> 2m <
17

==> m < 17/
2

==> m <
8.5

==> m = ( -inf,
8.5)

But m = positive
integer.

Then, m = { 1, 2, 3, 4, 5, 6, 7, 8
}

Case(2):

-(2m-5)
< 12

==> -2m + 5 <
12

==> -2m <
7

==> m >
-7/2

==> m = ( -7/2, inf)   which is impossible
because m is a positive integer.