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

Dec 17, 2016

$x = - 12$ and $x = 12$

#### Explanation:

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

$- 1 \times - \left\mid - x \right\mid = - 1 \times - 12$

$\left\mid - x \right\mid = 12$

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)

$- x = 12$

$- 1 \times - x = - 1 \times 12$

$x = - 12$

Solution 2)

$- x = - 12$

$- 1 \times - x = - 1 \times - 12$

$x = 12$