1. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 1 5 Minute Check Solve and graph the following. 1. 2. 3. -3t – 5 7

2. 2 What you will learn today  How to solve an absolute value equation  How to solve an absolute value inequality  How to graph the solution to an absolute value inequality

3. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 3 Absolute Value Equations and Inequalities The absolute value of a number x, written |x|, is the distance the number is from zero on the number line. The absolute value of a number is always positive (distance is always positive).

4. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 4 Question?  What are the possible values for x? |x| = 5

5. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 5 Question?  What are the possible values for x? |x| = 5 Which leads to the following “rule”. The absolute value equation |ax+b|=c, where c > 0, is equivalent to the compound statement ax + b = c or ax + b = -c.

6. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 6 Solving an Absolute Value Equation  Solve |2x – 5| = 9

7. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 7 You Try  Solve |2 – 4x| = 10

8. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 8 Inequality Rules  The inequality |ax + b| 0, means that ax + b is between –c and c. This is a compound “and” inequality. It is equivalent to –c<ax + b<c  The inequality |ax + b| > c, where c > 0, means that ax + b is beyond –c and c. This is an “or” compound inequality. It is equivalent to ax + b c.

9. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 9 Solving an Absolute Value Inequality Solve:|2x + 7| < 11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

10. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 10 You Try  Solve -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

11. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 11 Another Example  Solve -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

12. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 12 You Try  Solve: |-3x + 10| > 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

13. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 13 A Question  What is wrong with the following? |3x – 5| < -10

14. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 14 An Application  A cereal manufacturer has a tolerance of.75 ounce for a box of cereal that is supposed to weigh 20 ounces. Write and solve an absolute value inequality that describes the acceptable weights for 20 ounce boxes.

15. Objective: Section 1.7 Solving Absolute Value Equations and Inequalities 15 Homework  Page 53, problems 32-36 even, 42-46 even, 48, 50, 54, 68