The solutions of an absolute-value equation are given. What is the equation? x= b + or - 2a

Question

anonymous · Answer

what does $x=b+$ mean?

anonymous · Answer

ooh maybe it is 
$$x=b\pm2a$$

anonymous · Answer

Yep!

anonymous · Answer

if you start with 
$$|x-b|=2a$$ and solve for $x$ you get 
$x-b=2a$ or $x-b=-2a$ so $x=b\pm2a$

anonymous · Answer

Wowza you're smart! Thank you, but how did you know to start with that equation?

e.mccormick · Answer

You gave $x=b\pm 2a$ so s73 basically saw the answer.

If you want to work for the answers, you do it in reverse.  The $\pm$ being the key point.  All the $\pm$ stuff must be on one side of the equation.  Everything else on the other.

anonymous · Answer

Ohh gotcha that makes a lot of sense, thank you! I appreciate it!

e.mccormick · Answer

$x=b\pm 2a$

OK, so just 2a is after the $\pm$  It needs to be alone with its $\pm$

$x=b\pm 2a\implies $
$x-b=\pm 2a\implies $
$|x-b|= 2a $  This last step basically turning the $\pm$ back into |  |.  So undoing math... which there is a lot of.  =)

Glad you got it!

anonymous · Answer

Thank you, I fanned ya!