## Solving Inequalities

### Johnny WolfeSanta Rosa District Schools

#### Description

Student will solve and graph inequalities and absolute values.

#### Objectives

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Solving Inequalities (see attached file).

- Solving Inequalities Examples (see attached file).

- Solving Inequalities Worksheet (see attached file).

- Solving Inequalities Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Solving Inequalities Examples (see attached file).

2. Have marking pens (for overhead).

3. Have Solving Inequalities Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of Solving Inequalities Worksheet (see attached file) for each student.

5. Have enough copies of Solving Inequalities Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations. Note: This lesson does not address the following: irrational, real, and complex numbers; square roots, exponents, and appropriate inverse relationships. This lesson contains a checklist to assist the teacher in determining which students need remediation. The sole purpose of this checklist is to aide the teacher in identifying students that need remediation. Students who meet the ōCö criteria are ready for the next level of learning.

1. Describe the three ways to compare objects (see # 1 on attached file Solving Inequalities Examples). Answer student questions and comments.

2. Illustrate the trichotomy property (see # 2 on attached file Solving Inequalities Examples). Answer student questions and comments.

3. Present the trichotomy property as a rule (see # 3 on attached file Solving Inequalities Examples). Answer student questions and comments.

4. Discuss the addition and subtraction properties for inequalities (see # 4 on attached file Solving Inequalities Examples). Answer student questions and comments.

5. Illustrate the addition and subtraction properties for inequalities (see # 5 on attached file Solving Inequalities Examples). Answer student questions and comments.

6. Work example 6 (see attached file Solving Inequalities Examples). Answer student questions and comments.

7. Work example 7 (see attached file Solving Inequalities Examples). Answer student questions and comments.

8. Work example 8 (see attached file Solving Inequalities Examples). Answer student questions and comments.

9. Work example 9 (see attached file Solving Inequalities Examples). Answer student questions and comments.

10. Give students an inequality and multiply by a positive number (see # 10 on attached file Solving Inequalities Examples). Answer student questions and comments.

11. Give students an inequality and multiply by a negative number (see # 11 on attached file Solving Inequalities Examples). Answer student questions and comments.

12. Discuss multiplication and division properties for inequalities (see #12 on attached file Solving Inequalities Examples). Answer student questions and comments.

13. Illustrate the multiplication and division properties for inequalities (see # 13 on attached file Solving Inequalities Examples). Answer student questions and comments.

14. Work example 14 (see attached file Solving Inequalities Examples). Answer student questions and comments.

15. Work example 15 (see attached file Solving Inequalities Examples). Answer student questions and comments.

16. Discuss operational symbols and their meaning (see # 16 on attached file Solving Inequalities Examples). Answer student questions and comments.

17. Work example 17 (see attached file Solving Inequalities Examples). Answer student questions and comments.

18. Work example 18 (see attached file Solving Inequalities Examples). Answer student questions and comments.

19. Work example 19 (see attached file Solving Inequalities Examples). Answer student questions and comments.

20. Work example 20 (see attached file Solving Inequalities Examples). Answer student questions and comments.

21. Discuss with students what ōabsolute valueö represents (see # 21 on attached file Solving Inequalities Examples). Answer student questions and comments.

22. Work example 22 (see attached file Solving Inequalities Examples). Answer student questions and comments.

23. Work example 23 (see attached file Solving Inequalities Examples). Answer student questions and comments.

24. Work example 24 (see attached file Solving Inequalities Examples). Answer student questions and comments.

25. Work example 25 (see attached file Solving Inequalities Examples). Answer student questions and comments.

26. Work example 26 (see attached file Solving Inequalities Examples). Answer student questions and comments.

27. Work example 27 (see attached file Solving Inequalities Examples). Answer student questions and comments.

28. Work example 28 (see attached file Solving Inequalities Examples). Answer student questions and comments.

29. Discuss the empty set and inequalities (see # 29 on attached file Solving Inequalities Examples). Answer student questions and comments.

30. Discuss inequalities that are always true (see # 29 on attached file Solving Inequalities Examples). Answer student questions and comments.

31. Work example 31 (see attached file Solving Inequalities Examples). Answer student questions and comments.

32. Work example 32 (see attached file Solving Inequalities Examples). Answer student questions and comments.

33. Distribute the Solving Inequalities Worksheet (see attached file).

34. Distribute the Solving Inequalities Checklist (see attached file). Describe what constitutes an ōA,ö ōB,ö ōC,ö ōD,ö and an ōFö in the CHECKLIST.

35. The student will write their response on the worksheet.

36. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and scored according to ōSolving Inequalities Checklistö. These scores may be placed in the grade book.

#### Extensions

Draw number lines on the board and have student write inequality statements that match the number line