Question

Solving an Absolute Value Equation
What is the solution set of -|-x1 =-12?
no solution
{-12}
{12}
{-12, 12)

Answer 1

Answer:

Solution set = {-12, 12}

Step-by-step 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}