How do you solve #2|x + 4| = 8#?

1 Answer
smendyka
Aug 3, 2017

See a solution process below:

Explanation:

First, divide each side of the equation by #color(red)(2)# to isolate the absolute value function while keeping the equation balanced:

#(2abs(x + 4))/color(red)(2) = 8/color(red)(2)#

#(color(red)(cancel(color(black)(2)))abs(x + 4))/cancel(color(red)(2)) = 4#

#abs(x + 4) = 4#

The absolute value function takes any negative or positive 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

#x + 4 = -4#

#x + 4 - color(red)(4) = -4 - color(red)(4)#

#x + 0 = -8#

#x = -8#

Solution 2

#x + 4 = 4#

#x + 4 - color(red)(4) = 4 - color(red)(4)#

#x + 0 = 0#

#x = 0#

The solutions are: #x = -8# and #x = 0#

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