Your inquiry:

How did -4x = 4y - z + 11
turn into:
4x/4 = - 4y - z + 11/4

should correctly be stated as "4x/4 = -(4y -z + 11)/4" [note the parentheses clarify that the entire numerator is being divided by '-4']

...so both sides of the equation are being divided by '-4'