Question 868819
Rendering tags do not work on this way:   |2x-6|=|x+1|
Use "abs()" instead of the vertical bars.
{{{abs(2x-6)=abs(x+1)}}} which is abs(2x-6)=abs(x+1).


This might be less efficient logic, but you may have four conditions to examine.
2x-6>=0 and x+1>=0;
2x-6<0 and x+1>=0;
2x-6>=0 and x+1<0;
2x-6<0 and x+1<0.



{{{2x-6>=0}}} and {{{x+1>=0}}};
The abs values simply give 2x-6=x+1.
x-6=1
x=6+1
x=7


{{{2x-6<0}}} and {{{x+1>=0}}};
{{{abs(2x-6)=abs(x+1)}}} gives then
-(2x-6)=x+1
-2x+6=x+1
-2x-x+6=1
-3x=1-6
-3x=-5
{{{x=5/3}}}


{{{2x-6>=0}}} and {{{x+1<0}}};
This combination will give
2x-6=-(x+1)
2x-6=-x-1
3x-6=-1
3x=-1+6
3x=5
{{{x=5/3}}}


{{{2x-6<0}}} and {{{x+1<0}}}.
If both these expressions are negative, then the absolute value equation  produces this ...
-(2x-6)=-(x+1)
-(2x-6)(-1)=-(x+1)(-1)
2x-6=x+1
which goes exactly the way the first combination, with both expressions positive or zero, went.
x=7


***************************
ANSWER:  {{{highlight(x=7)}}} or {{{highlight(x=5/3)}}}   ****
***************************