First, add #color(red)(1)# to each side of the equation to isolate the absolute value function while keeping the equation balanced:
#color(red)(1) + 5 = color(red)(1) - 1 + abs(-5x + 4)#
#6 = 0 + abs(-5x + 4)#
#6 = abs(-5x + 4)#
The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
Solution 1:
#-6 = -5x + 4#
#-6 - color(red)(4) = -5x + 4 - color(red)(4)#
#-10 = -5x + 0#
#-10 = -5x#
#(-10)/color(red)(-5) = (-5x)/color(red)(-5)#
#2 = (color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5))#
#2 = x#
#x = 2#
Solution 2:
#6 = -5x + 4#
#6 - color(red)(4) = -5x + 4 - color(red)(4)#
#2 = -5x + 0#
#2 = -5x#
#2/color(red)(-5) = (-5x)/color(red)(-5)#
#-2/5 = (color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5))#
#-2/5 = x#
#x = -2/5#
The Solutions Are: #x = 2# and #x = -2/5#
