Solving Absolute Value Equations

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In math, the absolute value of a number is its distance from zero. Solve absolute value equations with tips from a math teacher in this free video on solving math problems.

Part of the Video Series: Solving Math Problems
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I'm Nancy ET Johnson, mathematics teacher. This is about how to solve absolute value equations. The absolute value of a number is its distance from zero disregarding whether it's to the left or to the right. So if we have an absolute value equation such as the absolute value of X is four, we want to know what number or numbers would give a distance of four from zero on the number line. Because both positive four and negative four are four units from zero, X equals four is a solution to this equation. X equals negative four is a solution to the equation. Just to understand this better, if we look at a number line and we see that one, two, three, four units away from zero we have four, its absolute value is four, or one, two, three, four units in the other direction at negative four, this number is also four units away from zero. So this equation has two solutions. X equals four. X equals negative four. Here's another absolute value equation. The absolute value of X plus two equals eight. Because absolute value means the distance from zero, and X plus two, eight means that this amount, if this expression could either be a positive eight, oh we need a plus in here, or it could be a negative eight, we can solve each of these equations independently to get the two solutions to this absolute value equation. X equals six, would be here, this is zero, X equals negative ten would be over here on our number line. So if I'm looking at an X of six, and I added two to that number, I would be here. And this is eight units away from zero. If I looked at this one, x equals negative ten, and added two, I would be here at a negative eight, also eight units away from zero. So we can verify that those solutions make sense. That's how to solve absolute value equations. I'm Nancy ET Johnson, mathematics teacher.

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