Question

The sum of five and some number `x` has an absolute value of 7. What are possible values of `x`?

Answer 1

`x = 2` and `x = -12`

Explanation:

Because this is an absolute equation, we must solve for the expression in the absolute bars being both a positive value and a negative value. This is because the absolute value of a number is always positive. Consider the following.

`| 5 + x | = 7`

For positive value in bars we have:

`5 + x = 7 => x = 2`

For negative value in bars we have:

`| -( 5 + x ) | = 7`

Removing bars:

`-( 5 + x ) = 7`

`-5 - x = 7 => x = -12`