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Absolute Value Equations and Inequalities

This document provides an overview of solving absolute value equations and inequalities. It explains that absolute value is the distance from 0 on the number line. For absolute value equations, two problems must be set up: one leaving everything as is without bars, and one leaving what's inside bars the same but changing the sign outside. Examples are provided of solving basic absolute value equations and inequalities, which require isolating the absolute value bars first before setting up two equations or problems. Practice problems are included for the reader to work through.

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Absolute Value Equations and Inequalities Notes and Examples
Absolute value is the distance a number is from 0 on the number line.
For an absolute value equation, you must set up TWO problems. •1. For the first problem, leave everything just like the question but drop the absolute value bars. •2. For the second problem, leave everything inside the bars the same, drop the absolute value bars, and change the sign of the number after the equal sign.
The next four slides have examples of some basic absolute value equations. Work through these on your guided notes sheet!
In this next set of examples, you will have to get the absolute value bars alone before you can write your two equations! Work through these on your guided notes sheet!
Now let’s review how to solve absolute value inequalities. In both cases, you still write TWO problems. However, you now switch the symbol AND the sign of the number when you write the second problem.
Two Kinds of Absolute Value Inequalities
The next three slides have examples of some basic absolute value inequalities. Work through these on your guided notes sheet!
You try the problems on the next slide. When you are done, check your answers using the final slides.
You Try!!
***Notice on this one that we had to switch our symbol after dividing by a negative on both sides!
You will notice that the graph looks like an “or” instead of an “and”. Since the shaded regions do not share anything in common, there is no solution.