SOLUTION: How do I solve |2z-3|=4z-1 for z?

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Question 334735: How do I solve |2z-3|=4z-1 for z?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

 |2z-3|=4z-1

Make two equations

2z-3 = +(4z-1)      or     2z-3 = -(4z-1)
2z-3 = 4z-1                2z-3 = -4z+1        
 -2z = 2                     6z = 4
   z = -1                     z = 4%2F6
                              z = 2%2F3

We must check the solutions because sometimes
we get extraneous solutions.

Check z = -1              Check z = 2%2F3
   
 |2z-3| = 4z-1               |2z-3| = 4z-1
|2(-1)-3| = 4(-1)-1         |2(2%2F3)-3| = 42%2F3-1
|-2-3| = -4-1               |4%2F3-3| = 8%2F3-1 
  |-5| = -5                 |4%2F3-9%2F3| = 8%2F3-3%2F3 
     5 = -5                   |-5%2F3| =  5%2F3 
That's false so                5%2F3 = 5%2F3     
z = -1 is NOT a               That's true, so the only
solution and must             solution is z = 2%2F3
be discarded.

Edwin