Question

What is the solution set of `-abs(-x)=-12`?

Answer 1

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

Explanation:

First, we must isolate the absolute value term while keeping the equation balanced:

`-1 xx -abs(-x) = -1 xx -12`

`abs(-x) = 12`

Now, because the absolute value function takes a positive or a negative number and transforms it to a positive number. we must solve the term within the absolute value for both the positive and negative of the term on the other side of the equation:

Solution 1)

`-x = 12`

`-1 xx -x = -1 xx 12`

`x = -12`

Solution 2)

`-x = -12`

`-1 xx -x = -1 xx -12`

`x = 12`