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Understanding Distances on Number Lines: An Absolute Value Application

Learn how to calculate distances on number lines using absolute value, including finding midpoints and translating distances into equations. Explore examples and solutions in this educational resource.

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Understanding Distances on Number Lines: An Absolute Value Application

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  1. Distances on Number LinesAn Application of Absolute Value

  2. |2x + 3| = -7 • What’s wrong? • Absolute value can not be equal to a negative number. • Therefore, there are no solutions.

  3. |2x + 3| = -7 • Distance of -7? 2x+3 0 2x+3

  4. Distance can never be negative • If the isolated absolute value is equal to a negative, the solution(s) will be extraneous.

  5. a + b m = 2 Midpoint • The average of the two coordinates.

  6. Midpoint • Find the midpoint between 4 and 10. 4 5 6 7 8 9 10

  7. Midpoint • Find the midpoint between -3 and 17. • Midpoint = 7

  8. Midpoint • Find the midpoint between -3 and -10. • Midpoint = -6.5

  9. Distance • If d is the distance between points a and b, then d = |a – b| = |b – a|. • It doesn’t matter which direction you subtract.

  10. Distance • What is the distance between • 4 and 7 |4 – 7| = 3 • 25 and 34 |25 – 34| = 9 • -2 and 6 |-2 – 6| = 8 Distance is the absolute value of the difference.

  11. Distance • Find the distance between 4 and 10. • The distance is 6 units. 4 5 6 7 8 9 10

  12. Distance • Find the distance between -5 and 9. • Distance = 14

  13. Distance • Find the distance between -3 and -21. • Distance = 18

  14. Distance • Find the distance between 27 and 71. • Distance = 44

  15. Translating to Equations • The distance from 4 to a number is 2. • There are 2 units between some number and 8. • A number’s distance from 0 is 6.

  16. Translating to Equations • The distance between a number x and -6 is 5. • x and -3 are 8 units apart.

  17. Translating • The distance between x and 5 is 4. • |5 – 4| = x • |x – 5| = 4 • |x – 5| = 1 • None of these

  18. Translating • The distance between 2 and a number is 6. • |6 – 2| = x • |x – 6| = 2 • |x – 2| = 6 • None of these

  19. Translating • 5 is 9 units from some number. • |5 – 9| = x • |x – 9| = 5 • |x – 5| = 9 • None of these

  20. Section 2.4 • pp. 56-57

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