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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