First, subtract #color(red)(3)# from each side of the equation to isolate the absolute value function while keeping the equation balanced:
#abs(-4x + 5) + 3 - color(red)(3) = 30 - color(red)(3)#
#abs(-4x + 5) + 0 = 27#
#abs(-4x + 5) = 27#
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:
#-4x + 5 = -27#
#-4x + 5 - color(red)(5) = -27 - color(red)(5)#
#-4x + 0 = -32#
#-4x = -32#
#(-4x)/color(red)(-4) = (-32)/color(red)(-4)#
#(color(red)(cancel(color(black)(-4)))x)/cancel(color(red)(-4)) = 8#
#x = 8#
Solution 2:
#-4x + 5 = 27#
#-4x + 5 - color(red)(5) = 27 - color(red)(5)#
#-4x + 0 = 22#
#-4x = 22#
#(-4x)/color(red)(-4) = (22)/color(red)(-4)#
#(color(red)(cancel(color(black)(-4)))x)/cancel(color(red)(-4)) = -22/4#
#x = -11/2#
The Solutions Are: #x = 8# and #x = -11/2#
