Question

Find all solutions (answers should be given in simplified form). Some answers may involve the number i.
*I will use lowercase l to represent absolute value lines.*

3 lx-1l + 4 = 19

We've never really worked with absolute value in solving equations before. Do I distribute the 3 to the x-1 as normal, or do something different?

This is my first idea:

3 lx-1l = 15

lx-1l = 5

x = -4, 6

Answer 1

No, you do not distribute the absolute value signs.
What you did is correct, i.e. keep the absolute value quantity intact, and eventually evaluate the value as either positive or negative.
|x-1|=5 means
x-1=5 => x=5+1=6
or
-(x-1)=5 => x=1-5=-4