We need to isolate the absolute value term. Therefore, first we will add #color(red)(9)# to each side of the equation to start to isolate the absolute value term while keeping the equation balanced:

#6abs(1 - 5x) - 9 + color(red)(9) = 57 + color(red)(9)#

#6abs(1 - 5x) - 0 = 66#

#6abs(1 - 5x) = 66#

Next, we will divide each side of the equation by #color(red)(6)#:

#(6abs(1 - 5x))/color(red)(6) = 66/color(red)(6)#

#(color(red)(cancel(color(black)(6)))abs(1 - 5x))/cancel(color(red)(6)) = 11#

#abs(1 - 5x) = 11#

The absolution value function takes any positive or negative term and transforms it into its positive form. Therefore we must find two solutions - one for the negative and one form the positive form of what the absolute value term is equated to.

Solution 1):

#1 - 5x = 11#

#1 - 5x - color(red)(1) = 11 - color(red)(1)#

#1 - color(red)(1) - 5x = 10#

#0 - 5x = 10#

#-5x = 10#

#(-5x)/color(red)(-5) = 10/color(red)(-5)#

#(color(red)cancel(color(black)(-5))x)/cancel(color(red)(-5)) = -2#

#x = -2#

Solution 2):

#1 - 5x = -11#

#1 - 5x - color(red)(1) = -11 - color(red)(1)#

#1 - color(red)(1) - 5x = -12#

#0 - 5x = -12#

#-5x = -12#

#(-5x)/color(red)(-5) = -12/color(red)(-5)#

#(color(red)cancel(color(black)(-5))x)/cancel(color(red)(-5)) = 12/5#

#x = 12/5#

The solution to this problem is #x = -2# and #x = 12/5#