Question

How do you solve `abs(v+8)-5=2`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(5)` to each side of the equation to isolate the absolute value function while keeping the equation balanced:

`abs(v + 8) - 5 + color(red)(5) = 2 + color(red)(5)`

`abs(v + 8) - 0 = 7`

`abs(v + 8) = 7`

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:

`v + 8 = -7`

`v + 8 - color(red)(8) = -7 - color(red)(8)`

`v + 0 = -15`

`v = -15`

• Solution 2:

`v + 8 = 7`

`v + 8 - color(red)(8) = 7 - color(red)(8)`

`v + 0 = -1`

`v = -1`

The Solution Set Is: `v = {-15, -1}`