1. 1 – 7 Solving Absolute Value Equations and Inequalities Objective: CA Standard 1: Students solve equations and inequalities involving absolute value.

2. The absolute value of x is the distance the number is from 0. Can the absolute value of x ever be negative? No

3. Solving an absolute value equation The absolute value equation where c > 0, is equivalent to the compound statement.

4. Solving an Absolute Value Equation Solve: Rewrite the absolute value equation as two linear equations and then solve each linear equation.

5. An absolute value inequality such as: can be solved by rewriting it as a compound inequality:

6. Transformation of Absolute Value Inequalities

7. Solving an inequality of the form  ax + b  < c The solution is all real numbers greater than –9 and less than 2. Graph the solution interval.

8. -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

9. Solving an inequality of the form  ax + b  c This absolute value inequality is equivalent to

10. The solutions are all real numbers less than or equal to –2 and greater than or equal to 10/3. Draw the graph of the solutions. Are the dots open or closed? Why?

11. Using Absolute Value in Real life In manufacturing applications, the maximum deviation of a product from some ideal or average measurement is called a tolerance.

12. Writing a Model for Tolerance A cereal manufacturer has a tolerance of 0.75 ounces 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. Verbal Model:  Actual Weight – Ideal weight   Tolerance

13. Labels: Actual weight = x Ideal weight = 20 Tolerance =.75 Algebraic Model:

14. Writing an Absolute Value Model You are a quality control inspector at a bowling pin company. A regulation pin weighs between 50 and 58 ounces. Write an absolute value inequality describing the weights you should reject. Verbal Model:  Wt. of pin – Avg. wt. of extreme weights   Tolerance

15. Labels:Weight of pin = w Average weight of extreme weights Tolerance: 58 – 4 = 4

16. Algebraic Model: You should reject a bowling pin if its weight w satisfies

17. HOMEWORK: