Question 908845
|3x-5|+2=5x-1

{{{abs(3x-5)=5x-1-2}}}
{{{abs(3x-5)=5x-3}}}


CASE, 3x-5 positive or zero.
{{{3x-5=5x-3}}}
{{{3x-5x-5=-3}}}
{{{-2x-5=-3}}}
{{{-2x=-3+5}}}
{{{-2x=2}}}
{{{highlight(x=-1)}}}


CASE, 3x-5 NEGATIVE.
{{{-3x+5=5x-3}}}
{{{-3x-5x+5=-3}}}
{{{-8x+5=-3}}}
{{{8x-5=3}}}
{{{8x=3+5}}}
{{{8x=8}}}
{{{highlight(x=1)}}}


SOLUTION:  {{{highlight(x=-1)}}}  OR  {{{highlight(x=1)}}},  ... but these do not work.


CHECK SOLUTION:
-------------------------------
|3x-5|+2=5x-1
{{{abs(3(-1)-5)+2=5(-1)-1}}}
{{{8+2=-6}}}
{{{10=-6}}}, clearly FALSE.
-
{{{abs(3*1-5)+2=5*1-1}}}
{{{abs(-2)+2=4}}}, <s>clearly FALSE.</s>
{{{2+2=4}}},  TRUE.


RESULT:  -1 fails; but +1 works.
ANSWER:  {{{highlight(x=1)}}}