For what values of t does the inequality hold? 5-3l 2t-3l

Given the inequality:

 5 - 3
l 2t -3 l < -16

First, we will solve the way we
solve any equation.

We need to isolate the absolute values
on the left side.

Let us subtract 5 from both
sides.

==> -3 l 2t -3 l <
-16-5

==> -3 l 2t -3 l <
-21

Now we will divide by -3 and reverse the
inequality.

==> l 2t -3 l >
-21/-3

==> l 2t -3 l >
7

Now we have two
cases:

Case(1):

(2t -3 )
> 7

==> 2t >
10

==> t >
5

==> t = (5,
inf)..............(1)

Case(2):

-(2t-3)
> 7

==> -2t +3 >
7

==> -2t >
4

==> t <
-2

==> t= (-inf,
-2)............(2)

From (1) and (2) we conclude
that:

t= (-inf, -2) U (5,
inf)

OR:

t=
R- [ -2, 5]