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Solving Absolute Value Inequalities: Graphing and Solution Sets

In this lesson, students will learn how to graph and write solution sets for absolute value inequalities, focusing on the example of |x - 3| < 6. We will explore the concepts of positive and negative forms, switching signs in negative forms, and the importance of using "or" for greater than inequalities. Students will engage in independent practice, checking their answers, and will conclude with an exit ticket that challenges them to identify the correct solution set for another example. Prepare for a quiz at the end of the week!

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Solving Absolute Value Inequalities: Graphing and Solution Sets

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  1. 3/29 Adv. Alg/Trig Bell Ringer Graph and write the solution set for |x – 3| < 6

  2. 3/29 News and Notes • Perfection: 4th • ACT Prep Tomorrow! • Missing Quizzes: • 2nd: Jazmyn • 4th: Raven, Victor, Arielle, Kyle 2 DAYS LEFT!!!!!

  3. This week’s plan • Mon: Absolute Value Inequalities (AND) • Today: Absolute Value Inequalities (OR) • Wed: Review Day • Thurs: Quiz • Fri: Day off!

  4. Example #1 2 min: Discuss what this inequality is asking for in words: The set of numbers that are greater than 4 units from zero.

  5. Example #1 What are a couple examples of numbers that are greater than 4 units from zero? Ex: 5, 6, 7, 8…, -5, -6, -7, -8…

  6. Example #1 You must SWITCH the sign when putting in negative form OR -4 4

  7. Let’s Summarize then do 1 more • Key #1: Positive and Negative Forms • Key #2: The sign on the negative form must be switched! • Key #3: When greater than, we need OR • Key #4: Graph and solution set are the values OUTSIDE!

  8. Example #2 You must SWITCH the sign when putting in negative form OR

  9. Example #2

  10. Check your answer • Plug a number back in to make sure it works!

  11. Independent Practice • You must check your answers on every single question!

  12. Exit Ticket • Which of the following is the correct solution set for |x – 5| > 7 • A. X > -2 OR x < 12 • B. 2 > x OR x < 12 • C. -2 < x < 12 • D. 12 < x OR x < 17

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