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extraneous solution

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1 Answer

Absolute value of x is always positive.
So |x|+6=2x-3 means
x+6=2x-3 only if x is positive              or -(x)+6=2x-3 only if x is negative
x+6-x=2x-3-x                                       or -x+6+x=2x-3+x
6=x-3                                                  or 6=3x-3
6+3=x-3+3                                          or 6+3=3x-3+3
x=9                                                    or 3x=9 i.e. 3x/3 = 9/3
x=9, here x is positive                       or x=3, here x is not negative.    
                                                             So this is an extraneous solution
Check the answer
|9|+6=2x9-3                                      or |3|+6=2x3-3
15=15. correct answer                  or 9=3 extraneous (incorrect) answer

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I assumed that absolute value of x+6=|x|+6.

If by "absolute value of x+6", you mean |(x+6)|, then you can get extraneous solution by solving

-(x+6)=2x-3 only if (x+6) < 0