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
