Question

Solving an Absolute Value Equation

What is the solution set of -|-x1 =-12?
no solution
{-12}
{12}
{-12, 12)

Answer 1

Solution set = {-12, 12}

Explanation:

Start by dividing both sides of the given equation by negative one, to get rid of the negative signs on both sides:

`-\,|-x|=-\,12\\|-x|=12`

Now we consider the two possible cases:

1) The expression inside the absolute value symbol is a positive number, then :

`|-x|=-x\\`

and replacing it in the equation, this becomes:

`|-x|=12\\-x=12\\x=-12`

which is our first answer.

2) The expression inside the absolute value symbol is a negative number, then :

`|-x|=x\\`

and replacing it in the equation, this becomes:

`|-x|=12\\x=12`

which is our second possible answer.

Then the set of solutions is: {-12, 12}