Question 984843
Check for the two possibilities of  z-1 being non-negative and being negative.


z-1 non-negative:
{{{abs(z-1)=7z-13}}}
{{{z-1=7z-13}}}
{{{-1=6z-13}}}
{{{12=6z}}}
{{{z=2}}}


z-1 NEGATIVE:
{{{abs(z-1)=7z-13}}}
Examine on a number line to help this seem sensible-------
{{{-(z-1)=7z-13}}}
{{{-z+1=7z-13}}}
{{{1=8z-13}}}
{{{8z=1+13}}}
{{{8z=14}}}
{{{z=14/8}}}
{{{z=7/4}}}


CHECK THIS LAST PART---
{{{abs(7/4-1)=7(7/4)-13}}}
{{{abs(7/4-4/4)=49/4-52/4}}}------NOT ACCEPTABLE


Only acceptable is {{{highlight(z=2)}}}.