Question

How do you solve `16=4abs(w+2)`?

Answer 1

See the entire solution process below:

Explanation:

First, divide both sides of the equation by `color(red)(4)` to isolate the absolute value function while keeping the equation balanced:

`16/color(red)(4) = (4abs(w + 2))/color(red)(4)`

`4 = (color(red)(cancel(color(black)(4)))abs(w + 2))/cancel(color(red)(4))`

`4 = abs(w + 2)`

`abs(w + 2) = 4`

The absolute value function takes any negative or positive term and transforms it into its positive form. Therefore we must solve the term within the absolute value function for both the negative and positive version of the term it is equated to.

Solution 1)

`w + 2 = -4`

`w + 2 - color(red)(2) = -4 - color(red)(2)`

`w + 0 = -6`

`w = -6`

Solution 2)

`w + 2 = 4`

`w + 2 - color(red)(2) = 4 - color(red)(2)`

`w + 0 = 2`

`w = 2`

The solution is: `w = 2` and `w = -6`