4|3x - 1| + 1 = 8
4|3x - 1| = 8 - 1
4|3x - 1| = 7
|3x - 1| = 7/4
Now lets think, we have 3x - 1 in module, so either its 7/4 or -7/4, we will have 7/4 at the end because of it, so we may have 2 solutions in this case:
3x - 1 = 7/4
and
3x - 1 = -7/4
So let's see:
3x - 1 = 7/4
3x = 7/4 + 1
3x = 11/4
x = 11/12
3x - 1 = -7/4
3x = -7/4 + 1
3x = -3/4
x = -1/4
So we have two possible answers, x = 11/2 and x = -1/4