Question

How do you solve `abs(-x+9)=4`?

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:

`-x + 9 = -4`

`-x + color(red)(x) + 9 + color(red)(4) = -4 + color(red)(4) + color(red)(x)`

`0 + 13 = 0 + x`

`13 = x`

`x = 13`

Solution 2:

`-x + 9 = 4`

`-x + color(red)(x) + 9 - color(red)(4) = 4 - color(red)(4) + color(red)(x)`

`0 + 5 = 0 + x`

`5 = x`

`x = 5`

The Solution Set Is: `x = {5, 13}`