Question

How do you solve `abs(-9+v)/8=3`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(8)` to isolate the absolute value function while keeping the equation balanced:

`color(red)(8) xx abs(-9 + v)/8 = color(red)(8) xx 3`

`cancel(color(red)(8)) xx abs(-9 + v)/color(red)(cancel(color(black)(8))) = 24`

`abs(-9 + v) = 24`

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:

`-9 + v = -24`

`color(red)(9) - 9 + v = color(red)(9) - 24`

`0 + v = -15`

`v = -15`

Solution 2:

`-9 + v = 24`

`color(red)(9) - 9 + v = color(red)(9) + 24`

`0 + v = 33`

`v = 33`

The Solutions Are: `v = -15` and `v = 33`