First, isolate the absolute value term while maintaining the balance of the equation:
#abs(1 + 5c) - 8 + color(red)(8) = -4 + color(red)(8)#
#abs(1 + 5c) - 0 = 4#
#abs(1 + 5c) = 4#
Because the absolute value function takes any positive or negative number and transforms it to the positive form of the number, we must solve the term within the absolute value for the positive and negative form of the equality.
Solution 1)
#1 + 5c = 4#
#1 - color(red)(1) + 5c = 4 - color(red)(1)#
#0 + 5c = 3#
#5c = 3#
#(5c)/color(red)(5) = 3/color(red)(5)#
#(color(red)(cancel(color(black)(5)))c)/color(red)(cancel(color(black)(5))) = 3/5#
#c = 3/5#
Solution 2)
#1 + 5c = -4#
#1 - color(red)(1) + 5c = -4 - color(red)(1)#
#0 + 5c = -5#
#5c = -5#
#(5c)/color(red)(5) = (-5)/color(red)(5)#
#(color(red)(cancel(color(black)(5)))c)/color(red)(cancel(color(black)(5))) = -1#
#c = -1#
