If I have $|3x| < x + 4$, I break it into two cases and get that $x<2$ and $x>-1$ and the question is done (I think).
In my solutions I have another problem that asks me to solve $|2x+3| = 2-x$,
and it is solved in the same way, except once the two solutions are found, they are plugged back into the equation to see if L.S. = R.S., and only one is valid.
My question is why is this necessary for that second problem but not for the first one? I don't understand. Thanks in advance!