How do you solve #|8- 3x | = 8#?

1 Answer
smendyka
Mar 19, 2018

See a solution process below:

Explanation:

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:

#8 - 3x = -#

#8 - color(red)(8) - 3x = -8 - color(red)(8)#

#0 - 3x = -16#

#-3x = -16#

#(-3x)/color(red)(-3) = (-16)/color(red)(-3)#

#(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = 16/3#

#x = 16/3#

Solution 2:

#8 - 3x = 8#

#8 - color(red)(8) - 3x = 8 - color(red)(8)#

#0 - 3x = 0#

#-3x = 0#

#(-3x)/color(red)(-3) = 0/color(red)(-3)#

#(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = 0#

#x = 0#

The Solution Set Is:

#x = (0, 16/3)#

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