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Snezhnost [94]
3 years ago
12

Solving an Absolute Value Equation

Mathematics
1 answer:
Andre45 [30]3 years ago
8 0

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}

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