SOLUTION: solve the following equation {{{ |2x-6|=|x+1| }}} I remember that the absol splits into positive and negative but then I get lost. Thank you in advanced

Question 868819: solve the following equation
AMP Parsing Error of [ |2x-6|=|x+1| ]: Invalid expression '|2\x-6|=|x+1|': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 203. .

I remember that the absol splits into positive and negative but then I get lost.
Thank you in advanced

Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Rendering tags do not work on this way: |2x-6|=|x+1|
Use "abs()" instead of the vertical bars.
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.

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

and ;
gives then
-(2x-6)=x+1
-2x+6=x+1
-2x-x+6=1
-3x=1-6
-3x=-5

and ;
This combination will give
2x-6=-(x+1)
2x-6=-x-1
3x-6=-1
3x=-1+6
3x=5

and .
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

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ANSWER: or ****
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Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
TIP: Use "abs(2x-6)" to get .

<---> and <--->

For the cases and both expressions have the same sign,
and we look for solutions to

As is within one of the cases above.
is a solution.

For the case ,
so ,
but so {{abs(2x-6)=-(2x-6=-2x+6}}} ,
and we look for solutions to

Since is within the case ,
is a solution.

Verification:
For :
and

For :
and

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