1 / 18

Directed Distance & Absolute Value

Directed Distance & Absolute Value. Warm Up: Solve the following absolute value equation. |2x – 3| = 13. Objective: To be able to find directed distances and solve absolute value inequalities. TS: Making Decisions after Reflection and Review.

cmckenzie
Download Presentation

Directed Distance & Absolute Value

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. Directed Distance &Absolute Value Warm Up: Solve the following absolute value equation. |2x – 3| = 13 Objective: To be able to find directed distances and solve absolute value inequalities. TS: Making Decisions after Reflection and Review The inside could have been+ or – 13 so need to solve both!

  2. Distance Between Two Points. What is the distance between the two values of 10 and 2? What is the distance between the two values of -102 and 80? So the distance between two points x1 and x2 is |x1 – x2| or |x2 – x1| 8 182

  3. Directed Distance The directed distance from a to b is b – a. Ex: Find the directed distance from 5 to -10 -10 – 5 -15 The directed distance from b to a is a – b. Ex: Find the directed distance from -10 to 5 5 – (-10) 15 -10 5 Had to go down, so -15 -10 5 Had to go up, so +15

  4. Midpoint The midpointbetween to values is a + b 2 Ex: Find the midpoint of the interval [1, 10] 1+10 2 5.5 10 6 5 0 1

  5. Absolute Value Is this statement true? Not true

  6. Absolute Value Think of absolute value as measuring a distance.

  7. Absolute Value Absolute Value: The distance a number is from zero on a number line. It is always positive or zero.

  8. Absolute Value ( ) The < sign indicates that the value is center around 0 and no more than 3 away.

  9. Absolute Value Now the subtraction of 2 has “translated” our center to 2. ( ) The < sign indicates that the value is centered around 2 and no more than 3 away. NOTICE: 2 is the midpoint of -1 and 5.

  10. Absolute Value ] [ The > sign indicates that the value is diverging from points on either side of 0.

  11. Absolute Value Now the subtraction of -3 has “translated” our center to -3. ] [ The > sign indicates that the value is diverging from points on either side of -3. NOTICE: -3 is the midpoint of -4 and -1.

  12. Writing an Absolute Value Ans: |x|≥4 • Write an absolute value inequality for the below intervals:(-∞, - 4]U[4, ∞) (-5, 5) (- ∞, 2)U(5, ∞) [-10, 20] Ans: |x|<5 Ans: |x – 3.5|>1.5 Ans: |x – 5|≤15

  13. Absolute Value What does this statement mean? ( )

  14. Absolute Value What does this statement mean? ] [

  15. Absolute Value Think of what we just saw. This picture would have two pieces, since the “distance” is greater.

  16. Absolute Value Think of what we just saw. This picture would have one piece between two numbers, since the “distance” is smaller.

  17. You Try Solve the following inequalities: • |2x|< 6 • |3x+1|≥4 • |25 – x|>20 Ans: (-3, 3) Ans: (-∞,-5/3] U [1,∞) Ans: (-∞,5) U (45,∞)

  18. Conclusion • Absolute value is the distance a number is from zero on a number line. • Two equations are necessary to solve an absolute value equation. • Two inequalities are necessary to solve an absolute value inequality.

More Related