# 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.

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Expert Answers

lemjay | Certified Educator

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

`5=|2z+3|`

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.

`+-5-3=2z+3-3`

`+5-3=2z`

And divide both sides by 2.

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

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

So,

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

and

`z=(-5-3)/2=(-8)/2=-4` **Hence, the values of z are -4 and 1.**