Absolute Value Equations and Inequalities

1. Absolute Value Equations and Inequalities Lesson 2.5

2. Absolute Value Function • Whatever you put into the functioncomes out positive -3 +7 +7 +3

3. Absolute Value Function • Definition Use the abs( ) function on your calculator

4. Absolute Value Function • Note the graph of y = | x | • Table of values

5. Absolute Value Equation • Let k be a positive number • Then means … • So we just solve two equations • Try it Solve analytically Solve graphically

6. Absolute Value Inequalities • |a x + b | < k is equivalent to • - k < a x + b < k • - k < a x + b and a x + b < k 7

7. ) ) Absolute Value Inequalities • |a x + b | > k is equivalent to • a x + b < -k or a x + b > k 7

8. Try It Out! • |15 – x | < 7 • Solve symbolically • |5x – 7 | > 2 • Show graphical solution

9. Application • Lou Scannon, the human cannon ball plans to travel 180 feet and land squarely on a net with a 70 foot long safe zone. • What distances D can Lou travel and still land safely on the net? • Use an absolute value inequality to describe the restrictions on D

10. Assignment • Lesson 2.5 • Page 154 • Exercises 1 – 53 EOO 73, 75, 83