First, subtract #color(red)(3)# from each side of the equation to isolate the absolute value term while keeping the equation balanced:
#abs(3 - 3t) + 3 - color(red)(3) = 15 - color(red)(3)#
#abs(3 - 3t) + 0 = 12#
#abs(3 - 3t) = 12#
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:
#3 - 3t = 12#
#3 - color(red)(3) - 3t = 12 - color(red)(3)#
#0 - 3t = 9#
#-3t = 9#
#(-3t)/color(red)(-3) = 9/color(red)(-3)#
#(color(red)(cancel(color(black)(-3)))t)/cancel(color(red)(-3)) = -3#
#t = -3#
Solution 2:
#3 - 3t = -12#
#3 - color(red)(3) - 3t = -12 - color(red)(3)#
#0 - 3t = -15#
#-3t = -15#
#(-3t)/color(red)(-3) = (-15)/color(red)(-3)#
#(color(red)(cancel(color(black)(-3)))t)/cancel(color(red)(-3)) = 5#
#t = 5#
The Solution Is:
#t = {-3, 5}#