How to Solve Absolute Value Inequalities?
Solve + Graph + Write with 13 Examples!

This lesson is all about putting two of our known ideas, Absolute Value and Inequalities, together in order to Solve Absolute Value Inequalities.

Now, we know that Absolute Value is the distance from zero, and an Inequality is a comparison between two or more things, and all we’re going to do is take our solving techniques from both of those lessons and put them together!

How are we going to do this?

We are going to imagine every Absolute Value Inequality is a boat, and we are Navy officers rowing to find land.

In fact, I want you to envision the Absolute Value expression is the row boat and the Inequality symbol represents your oars.

And if we use this image to help us solve all Absolute Value Inequalities, we will find that these types of problems are quite easy.

But I must caution you…

… whenever we are solving absolute value inequalities, we must first isolate the absolute value expression (i.e., our boat) on one side of the inequality before separating the inequality into either an “and” or “or” inequalities (i.e., our oars).

After we’ve mastered how to solve Absolute Value Inequalities, we are going to learn how to write an equation or inequality involving absolute value to describe a graph or statement.

Now, when solving Absolute Value Inequalities, we must never lose sight of the fact that we are dealing with distance from zero. Therefore, we can never take the absolute value of a negative number, so be on the lookout for this trick type question, as Purple Math calls it.

I am confident that after walking through all of these examples in detail you will be an Absolute Value Inequalities Admiral!

Solving Absolute Value Inequalities – Video

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