How do I solve |3-3T|+3=15 ?

1 Answer
Feb 8, 2018

See a solution process below:

Explanation:

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}#