How would you solve these absolute value equations?

Question

1.|3x-1|=|x+4|
2.|3/k-1|=4

Answer 1

case1
3x-1 = x+4
2x = 5
x = 5/2

case 2
3x-1 = -x - 4
4x = -3
x = -3/4

There are also cases 3 and 4.
These would be (-3x-1) = -(x+4)
and
-(3x-1) = x+4

but they yield the same answers as we already found

2. |3/k - 1| = 4

3/k - 1 = 4 OR 3/k - 1 = -4
3 - k = 4k or 3 - k = -4k
3 = 5k or 3 = -3k
k = 3/5 or k = -1