Assuming the equation is
[tex] |c|+5=9 [/tex]
you can subtract 5 from both sides to get
[tex] |c| = 4 [/tex]
Which means that the "positive version" of c has to be 4.
So, if c is positive, it must be 4 itself.
If c negative, it must be -4, so that when you change its sign it becomes 4 again.
So, the answer is [tex] c = \pm 4 [/tex]
