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

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 x 1 and x 2 is |x 1 – x 2 | or |x 2 – x 1 | 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

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

5. Absolute Value Not true Is this statement 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 ( ) The < sign indicates that the value is center 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 ] [ 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 1)Write an absolute value inequality for the below intervals: (-∞, - 4]U[4, ∞) (-5, 5) (- ∞, 2)U(5, ∞) [-10, 20]

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

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

15. Absolute Value

17. You Try Solve the following inequalities: 1) |2x|< 6 2) |3x+1|≥4 3) |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.