Originally Posted by
masters Hello Magentarita,
Case 1:
$\displaystyle x-3=(3x+2)-1$
$\displaystyle x=-2$
This solution does not work with the original equation, so throw it out.
Case 2:
$\displaystyle x-3=-(3x+2)-1$
$\displaystyle x=0$
This solution does not work with the original equation, so throw it out.
Case 3:
$\displaystyle -(x-3)=(3x+2)-1$
$\displaystyle \boxed{x=\frac{1}{2}}$
This solution works, so keep it.
Case 4:
$\displaystyle -(x-3)=-(3x+2)-1$
$\displaystyle \boxed{x=-3}$
This solution works, so keep it.