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Understanding Absolute Value Equations | Distance in Math

Learn about absolute value equations, solving strategies, and examples with absolute values indicated by vertical bars. Practice evaluating expressions and solving equations with absolute values in this comprehensive lesson.

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Understanding Absolute Value Equations | Distance in Math

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  1. Transparency 4a

  2. Splash Screen

  3. Definition of Absolute Value • “Absolute value” means “distance away from zero” on a number line • Distance is always positive or zero • Absolute value is indicated by placing vertical parallel bars on either side of a number or expression Examples: The distance away from zero of -3 is shown as: The distance away from zero of 3 is shown as: The distance away from zero of u is shown as: = u

  4. Absolute Value Equation • An equation that has a variable contained within absolute value symbols • Examples: | 2x – 3 | + 6 = 11 | x – 8 | – | 7x + 4 | = 0 | 3x | + 4 = 0

  5. Solving Absolute Value Equations • Isolate one absolute value that contains an algebraic expression, | u | • If the other side is negative there is no solution (distance can’t be negative) • If the other side is zero, then write: • u = 0 and Solve • If the other side is “positive n”, then write: • u = n OR u = - n and Solve • If the other sideis another absolute value expression, | v |, then write: • u = v OR u = - v and Solve

  6. Example of SolvingAbsolute Value Equation

  7. Example of SolvingAbsolute Value Equation

  8. Example of SolvingAbsolute Value Equation

  9. Lesson 4 Contents Example 1Evaluate an Expression with Absolute Value Example 2Solve an Absolute Value Equation Example 3No Solution Example 4One Solution

  10. Evaluate Replace x with 4. Simplify –2(4) first. Subtract 8 from 6. Add. Example 4-1a Answer: The value is 4.7.

  11. Evaluate Example 4-1b Answer: –13.7

  12. Solve Check your solutions. Case 1 Case 2 or Check: Answer: The solutions are5 or –11. Thus, the solution set is Example 4-2a

  13. Solve Check your solutions. Answer: Example 4-2b

  14. Solve Original equation Subtract 5 from each side. Example 4-3a This sentence is never true. Answer: The solution set is .

  15. Solve Example 4-3b Answer: 

  16. Solve Check your solutions. Case 1 Case 2 or There appear to be two solutions, 11 or Example 4-4a

  17. Check: Answer: Since , the only solution is 11. The solution set is {11}. Example 4-4b

  18. Solve Example 4-4c Answer: {6}

  19. End of Lesson 4

  20. Homework • Pages 30 – 31 #’s 18 – 26, 29 – 40 Due Tomorrow (9/9/09)

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