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#
