# What is C values if 5- 3l 2C +5 l < 13

Asked on by yasmin130

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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)

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