What is C values if 5- 3l 2C +5 l

5 - 3 l 2C+5 l < 13

To solve
for C, first we need to isolate the absolute value on the left
side.

First, we wiil subtract 5 from both
sides.

==> -3 l2C + 5 l < 13 -
5.

==>  -3 l 2C + 5 l <
8

Now we will divide by -3.

( Notice
that when dividing or multiplyin by a negative number, we need to reverse the
inequality).

==> l 2C + 5 l >
-8/3

Now we have two cases:

(
Case(1):

2C + 5 > - 8/
3

==> 2C > -8/3  -
5

==> 2C > -23/3

Now we
will divide by 2:

==> C >
-23/6

Then, C = ( -23/6, inf).

Case(2):

- (
2C + 5) > -8/3

==> -2C - 5 >
-8/3

==> -2C > -8/3 +
5

==> -2C >  7/3

Divide
by -2 and reverse :

==> C <
-7/6

Then, C = ( - inf , -7/6)