Question 334735
<pre><b>
 |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 = {{{4/6}}}
                              z = {{{2/3}}}

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

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

Edwin</pre>