SOLUTION: /2z-3/=4z-1

Question 652268: /2z-3/=4z-1
Answer by Shana-D77(132) (Show Source): You can put this solution on YOUR website!
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)
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