How do you solve #|3z + 1| = | z - 5|#?

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Answer 1 · 2017-09-13T13:46:52

Use the alternate form:

#sqrt((3z+1)^2) = sqrt((z-5)^2)#

Given: #|3z + 1| = | z - 5|#

An alternate form is:

#sqrt((3z+1)^2) = sqrt((z-5)^2)#

The arguments under the radicals must be equal:

#(3z+1)^2 = (z-5)^2#

Expand the squares:

#9z^2 + 6z+1 = z^2-10z + 25#

Combine like terms:

#8z^2 + 16z-24 = 0#

Divide both sides by 8:

#z^2 + 2z-3 = 0#

Factor

#(z+3)(z-1) = 0#

#z = 3 and z = 1#

Here is a graph of the two functions:

www.desmos.com/calculator

Please observe that the two graphs intersect at #z = -3# an #z = 1#