1. Module 1 ~ Topic 4 Solving Absolute Value Inequalities Table of Contents  Slides 2-3: How to Solve Absolute Value Inequalities  Slides 4-5: How to write the answer appropriately  Slide 6: Rules  Slides 7-10: Examples  Slide 11: Practice Problems Audio/Video and Interactive Sites  Slide 12: Interactive

2. To solve Absolute Value Inequalities 1.Isolate the absolute value expression on one side. a)To do this, do any addition or subtraction first b)Then do any multiplication or division last. ** If you multiply or divide by a negative number, make sure you flip the inequality sign in this step. 2. a) Set up two inequalities if the absolute value expression is opposite a 0 or a positive number: For the first equation, rewrite the expression that is inside the bars (but do not use the bars) and set it up using the same inequality sign that is in the original problem. For the second equation, rewrite the expression that is inside the bars again (but do not use the bars) and set it up using the opposite inequality sign of the one in the original problem. WRITE THE ANSWER IN CORRECT FORM b) If the isolated absolute value expression is set up to be less than a negative number, there is no solution. You can stop.

3. Absolute Value Inequalities Explanation and Examples There are several rules that apply to absolute value inequalities. You must be very careful when solving and you also must restate your answers correctly before submitting your assignments. There are several rules that apply to absolute value inequalities. You must be very careful when solving and you also must restate your answers correctly before submitting your assignments.

4. Two Types of Answers ANDOR “AND” problems include all numbers between the two solutions found on the number line. “OR” problems include all numbers in opposite directions on the number line. 0 AABB

5. Two Types of Answers AND OR 0 AABB Notice, visually, how the answer resembles the graph. All answers (x) are Between A AND B. Notice: The word “and” is NOT in the answer. All answers, x, are either less than A OR greater than B. Notice the word “or’ is in the answer.

7. Examples: Absolute Value Inequalities 0-8 8 The solution to | x | > 8 is: x 8 Use a number line to help you with the solution.

8. Notice: You will be dividing by a negative number, don’t forget to flip the sign!! 0-2 2 The solution to | -4x | > 8 is: x 2 Use a number line to help you with the solution.

9. Notice: You will be dividing by a negative number, don’t forget to flip the sign!! -90 The solution is Use a number line to help you with the solution.

10. Since the absolute value is shown to be less than 0, this problem has a solution of “No Solution”.

11. Solve the ProblemSolutionSolution in Interval Form If you are unable to get these answers, please ask your instructor for help before attempting the assignments.

12. More Explanation and Examples Interactive Practice Problems