Question

How do you solve `abs(4n + 7) = 1`?

Answer 1

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:

`4n + 7 = -1`

`4n + 7 - color(red)(7) = -1 - color(red)(7)`

`4n + 0 = -8`

`4n = -8`

`(4n)/color(red)(4) = -8/color(red)(4)`

`(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) = -2`

`n = -2`

Solution 1:

`4n + 7 = 1`

`4n + 7 - color(red)(7) = 1 - color(red)(7)`

`4n + 0 = -6`

`4n = -6`

`(4n)/color(red)(4) = -6/color(red)(4)`

`(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) = -3/2`

`n = -3/2`

The Solution Set Is:

`n = {-2, -3/2}`