Solve Equations with Absolute Value

This lesson shows how to solve equations involving absolute value.

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transcript:

Welcome to Your Tutor Online video lessons. Today we will learn how to solve equations that have an absolute value in them.

As a review, absolute value refers to how far away a number is from zero. To put it simply, the absolute value makes a number positive no matter what. Three is three units away from zero. Negative four is four units away from zero. So the absolute value of three is three, and the absolute value of negative four is four. Three stays positive, number four becomes positive.

What if there is a variable inside the absolute value sign? Well, in our order of operations, we want to treat the absolute value sign just like we would parentheses. So simplify everything inside them first, and move everything you can to the other side. In this example, 3 times the absolute value of x plus 2 is equal to 9, we can divide both sides by 3 and we are left with the absolute value of x plus 2 is equal to 3. When you get the absolute value all by itself on one side, you are done with the simplification.

Now we need to split this equation into two separate equations. For the first one, simply drop the absolute value signs. We have x plus 2 is equal to 3. For the other equation drop the absolute value signs and this time make the other side of the equation negative. Or if its already negative make it positive, just flip the sign of the other side of the equation.

Solve each equation that you came up with. On the left x is equal to 1 and on the right x is equal to negative 5. So for absolute value equations we will have two solutions, In this case x is equal to 1 or x is negative 5.

I hope you found this lesson useful. If you have any questions leave a comment on the blog at www.YourTutorOnline.com If you have any lessons suggestions send an email to podcast[at]yourtutoronline.com Thanks for watching, class dismissed.