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Absolute Value Equations and Inequalities are most easily related to Distance. We have an Algebra 2 Lesson that does a good job of explaining this. It can be found here: Absolute Value Functions and Graphs  Real World Applications
How Tough Are Absolute Value Equations and Inequalities?
When it comes to Algebra 1 this is probably one of the toughest lessons for the students all year. They have to have mastered how to solve both Absolute Value Equations and Inequalities separately. Then they have to put both of those skill sets together and remember all the rules that go with them. There are a lot for both.
 When to flip the inequality sign.
 When to split the two equations for Absolute Value.
 How to isolate the absolute value portion of the problem.
 How to graph each.
It is a lot for them to handle at once...
Use Multiple Days!
I always cover this lesson over multiple days and then sprinkle them in throughout the rest of the year.
Though, it is a very niche lesson meaning it doesn't get used as much as some other topics. It is heavily covered in Algebra 2. They have to be prepared for that.
Here is your free content for this lesson!
Absolute Value Equations and Inequalities  PDFs
37 Absolute Value Equations and Inequalities Worksheet (Free)
37 Solving Absolute Value Equations and Inequalities Worksheet Answer Key (Members Only)
37 Bell Work  Absolute Value Equations and Inequalities (Free)
37 Exit Quiz  Absolute Value Equations and Inequalities (Free)
37 Guide Notes SE  Absolute Value Equations and Inequalities (Free)
37 Guided Notes Teacher Edition (Members Only)
37 Lesson Plan (Members Only)
37 Online Activities (Members Only)
37 Video Lesson (Members Only)
37 Slide Show  Absolute Value Equations and Inequalities (Free)
37 Project (Members Only)
Absolute Value Equations and Inequalities Worksheet Doc & PowerPoint
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Absolute Value Equations and Inequalities Worksheet 37
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Solving Inequalities Worksheet
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Solving Absolute Value Equations and Inequalities Worksheet Answer Key Algebra 1
Equations and Inequalities pdf