Question 652268
the absolute value of anything can be equal to either a number or the opposite of a number.  Ex: |-5| = 5 (opposite of what's inside) |5| = 5 (exactly what's inside)

So, |2z - 3| = 4z - 1 or |2z - 3| = -(4z - 1)

2z - 3 = 4z - 1     or    2z - 3 = -4z + 1

Solve both equations for z, you get...

z = -1      and                z = 2/3

Wait!  We have to throw out -1 because |2(-1) - 3| = |-5| = 5 and the other side would be 4(-1) - 1 = -5.  5 does not equal -5!

So the only answer that works is z = 2/3 (make sure you check both as sometimes neither may work)