I'm really confused about absolute value-
What is an extraneous solution? I have to solve for x, then check for an extraneous solution with |2x+12|=4x

And also, how do I transform an absolute value equation into two linear equations? One of the problems is:
Transform the absolute value equations into two linear equations. Then Solve |x-10|=17
I know what I would do if i just had to find x, but how do change it into 2 linear equations?

Question

I'm really confused about absolute value-
What is an extraneous solution? I have to solve for x, then check for an extraneous solution with |2x+12|=4x

And also, how do I transform an absolute value equation into two linear equations? One of the problems is: 
Transform the absolute value equations into two linear equations. Then Solve |x-10|=17 
I know what I would do if i just had to find x, but how do change it into 2 linear equations?

freckles · Answer

You have to solve two equations because |2x+12|= either 2x+12 or -(2x+12) 

so we have 
2x+12=4x             or              -(2x+12)=4x
You have to solve both of these equations.
Then to figure out what the extraneous solution (the extra solution; the solution that really isn't a solution to the original equation |2x+12|=4x ) you need to plug in the values of x you found from 2x+12=4x and -(2x+12)=4x .
If one of the values you found for x does not check out, then it is an extraneous solution (again which is not really a solution).

anonymous · Answer

Okay, I solved for x for both of them and the second one didn't equal each other, so do I write the extraneous solution as |2(-2) + 12| =4(-2) ?