How do you solve #4|-6x + 6| + -3 = 93#?

1 Answer
smendyka
Dec 5, 2016

#x = -3# and #x = 5#

Explanation:

When solving an absolute value problem the first step is to isolate the absolute value on one side of the equation:

#4abs(-6x + 6) + -3 + 3 = 93 + 3#

#4abs(-6x + 6) + 0 = 96#

#4abs(-6x + 6) = 96#

#(4abs(-6x + 6))/4 = 96/4#

#(cancel(4)abs(-6x + 6))/cancel(4) = 24#

#abs(-6x + 6) = 24#

Now because the absolute value function converts both negative and positive numbers to a negative number we must solve the term within the absolute value for both #24# and #-24#:

#-6x + 6 = 24#

#-6x + 6 - 6 = 24 - 6#

#-6x + 0 = 18#

#-6x = 18#

#(-6x)/-6 = 18/(-6)#

#(cancel(-6)x)/cancel(-6) = -3#

#x = -3#

and

#-6x + 6 = -24#

#-6x + 6 - 6 = -24 - 6#

#-6x + 0 = -30#

#-6x = -30#

#(-6x)/-6 = (-30)/(-6)#

#(cancel(-6)x)/cancel(-6) = 5#

#x = 5#

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