1 / 12

Understanding Absolute Value Equations: A Comprehensive Review

In this unit on absolute value equations, we explore the concept of absolute value, defined as the distance of a number from zero on a number line. With practical examples, we learn how to solve absolute value equations by isolating the absolute value expression and splitting the problem into two cases. Through step-by-step guidance, we cover various equations and emphasize that not all absolute value equations have solutions, particularly those resulting in negative values. Homework exercises are included for practice.

jariah
Download Presentation

Understanding Absolute Value Equations: A Comprehensive Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Absolute Value Equations Unit 3, Day 5

  2. Review of Absolute Value http://www.brainpop.com/math/numbersandoperations/absolutevalue/preview.weml

  3. 5units The absolute-value of a number is that numbers distance from zero on a number line. For example, |–5| = 5. 1 6 4 3 0 1 2 3 4 5 5 2 6 Both 5 and –5 are a distance of 5 units from 0, so both 5 and –5 have an absolute value of 5.

  4. How to Solve Absolute Value Equations: Isolate the absolute-value expression Split the problem into two cases.

  5. Solve the equation. |x| –3 = 4 + 3 +3 |x| = 7 x = 7 –x = 7 –1(–x) = –1(7) x = –7

  6. Solve and check |a| – 3 = 5 |a| – 3 + 3 = 5 + 3Add 3 to each side. |a| = 8 Simplify. a = 8 or a = –8

  7. +2 +2 Solve the equation. |x 2| = 8 x 2= 8 x 2= 8 +2 +2 x = 10 x = 6

  8. Solve |3c – 6| = 9 3c – 6 = 9 3c – 6 = –9

  9. |x + 7| = 8 x + 7 = –8 x + 7 = 8 – 7 –7 – 7 –7 x = –15 x = 1

  10. CAREFUL! Not all absolute-value equations have solutions. If an equation states that an absolute-value is negative, there are no solutions.

  11. Solve the equation. 2  |2x 5| = 7 2 2  |2x 5| = 5 1 1 |2x  5| = 5 Absolute values cannot be negative. This equation has no solution.

  12. Homework p.237, #1-21

More Related