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
