Find values of z for which f(z) = 5 given f(z) = l 2z + 3 l   l 2z + 3 l : those lines are the symbols used in absolute values.

Expert Answers
lemjay eNotes educator| Certified Educator

To solve for z, plug-in the value of f(z).


Then, apply the property of absolute value which is if |x|=a, then `x=+-a` .

So removing the absolute value sign results to:

`+-5 = 2z + 3`

Then, isolate z. To do so, subtract both sides by 3.



And divide both sides by 2.

`(+-5-3)/2 =(2z)/2`



`z=(5-3)/2=2/2 = 1`



Hence, the values of z are -4 and 1.