solving equations with two absolute value brackets

Question

|x+4| = |x-2|
so i want to know how to do this? do i always have to write out the four piecewise possibilities? that be ++ -+ and +-

++
x+4 = x-2
4 = -2 not solution

-+
-(x+4) = x-2
-x-4 = x-2
-4 = 2x-2
-1 = x solution

+-
x+4 = -(x-2)
x+4 = -x+2
2x+4 = 2
x = -1 solution

Answer 1

i forgot put the other one

--
-(x+4) = -(x-2)
-x+4 = -x+2
4 = 2 no solution

Answer 2

you are correct.