Question

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

Answer 1

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`