Question

How do you solve `abs(x-3)-6=2`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(6)` to each side of the equation to isolate the absolute value function while keeping the equation balanced:

`abs(x - 3) - 6 + color(red)(6) = 2 + color(red)(6)`

`abs(x - 3) - 0 = 8`

`abs(x - 3) = 8`

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:

`x - 3 = -8`

`x - 3 + color(red)(3) = -8 + color(red)(3)`

`x - 0 = -5`

`x = -5`

Solution 2:

`x - 3 = 8`

`x - 3 + color(red)(3) = 8 + color(red)(3)`

`x - 0 = 11`

`x = 11`

The Solution Set Is:

#x = {-5, 11}

Answer 2

`{x-3>0`
`{-x+3>0`

So it's either `x-3` or `-x+3` and you put both of these separate

`x-3-6=2` from where `x=11`

and

`-x+3-6=2` from where `x=-5`