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# Module 3 lesson 12

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### Module 3 lesson 12

1. 1. Module 3 Lesson 12.notebook 1/24/14 Module 3 Lesson 12 January 28, 2014 Homework: Problem Set 12 #1-3 AIM: Properties of Inequalities Do Now Lesson 11 Exit Ticket 1
2. 2. Module 3 Lesson 12.notebook January 28, 2014 2
3. 3. Module 3 Lesson 12.notebook January 28, 2014 Exit Ticket Solution: 3
4. 4. Module 3 Lesson 12.notebook January 28, 2014 Homework Answers 4
5. 5. Module 3 Lesson 12.notebook January 28, 2014 Homework Answers 5
6. 6. Module 3 Lesson 12.notebook January 28, 2014 Homework Answers 6
7. 7. Module 3 Lesson 12.notebook January 28, 2014 Opening Exercise Sprint 7
8. 8. Module 3 Lesson 12.notebook January 28, 2014 8
9. 9. Module 3 Lesson 12.notebook January 28, 2014 9
10. 10. Module 3 Lesson 12.notebook January 28, 2014 1.) What numbers could you substitute for the variable in this mathematical sentence? x>3 2.) What numbers can not be substituted for x? x > 3 is an INEQUALITY- a mathematical sentence that contains 10
11. 11. Module 3 Lesson 12.notebook January 28, 2014 means the inequality symbol  stays the same means the inequality symbol  switches less than with greater  than and less than or equal to  with greater than or equal to 11
12. 12. Module 3 Lesson 12.notebook January 28, 2014 12
13. 13. Module 3 Lesson 12.notebook January 28, 2014 ­3 4 + ­3 > ­3 + ­3        1 > ­6 > 2 3 ­ 2 > 2 ­ 2      1 > 0 ­3 > ­4 ­3 ­ (­1) > ­4 ­ (­1)          ­2 > ­3 4 3 ­2 > < 5 ­2 + 1 < 5 + 1 ­1 < 6 Preserved Preserved Preserved Preserved 13
14. 14. Module 3 Lesson 12.notebook January 28, 2014 14
15. 15. Module 3 Lesson 12.notebook January 28, 2014 4 > ­3 4(­1) > (­3)(­1)    ­4 < 3 3 > 2 3(­1) > 2(­1)    ­3 < ­2 ­3 > ­4 ­3(­1) > (­4)(­1)        3 < 4 Reversed ­2 < 5 ­2(­1) < 5(­1)        2 > ­5 Reversed Reversed Reversed 15
16. 16. Module 3 Lesson 12.notebook January 28, 2014 16
17. 17. Module 3 Lesson 12.notebook 4 3 > > ­3 2 January 28, 2014 4(2) > (­3)(2)    8 > ­6 3 > 2 2    2 Preserved Preserved    1.5 > 1 ­3 > ­4 ­3 > (­4)        Preserved  ­6 > ­8 ­2 < 5 ­2(3) < 5(3)       ­6 < 15 Preserved 17
18. 18. Module 3 Lesson 12.notebook January 28, 2014 18
19. 19. Module 3 Lesson 12.notebook 4 3 > > ­3 January 28, 2014 4(­3) > (­3)(­3)    ­12 < 9 3 > 2 ­2   ­2 2    ­1.5 < ­1 Reversed Reversed ­3 > (­4) ­3 > ­4 Reversed        6 < 8 ­2 < ­2(   ) < 5(   ) 5        1 > ­2.5 Reversed 19
20. 20. Module 3 Lesson 12.notebook January 28, 2014 Discussion To summarize, when did the inequality symbol  change and when did it stay the same? Preserved Reversed 1.) Add or subtract any number 1.) Multiply or divide by a 2.) Multiply or divide by a negative positive 20
21. 21. Module 3 Lesson 12.notebook 2 + 1 < 5 + 1       3 < 6 January 28, 2014 2(­1) < 5(­1)      ­2 > ­5 ­4 ­ 1 > ­6 ­ 1 ­4 > ­6 ­2    ­2       ­5 > ­7       2 < 3 ­1(6)    2(6)     ­6    12 ­5 < ­4        ­5 + 5 < ­4 + 5       0 < 1 Multiplying by a  negative reverses  the symbol. Dividing by a  negative reverses  the symbol. ­1(­4)    2(­4) Multiplying by a  negative reverses        4    ­8 the symbol. ­5 < ­4 ­1    ­1       5 > 4 Dividing by a  negative reverses  the symbol. 21
22. 22. Module 3 Lesson 12.notebook January 28, 2014 Closing: 1.) What does it mean for an inequality to be preserved? What does it mean for the inequality to be reversed? 2.) When does a greater than become a less than? 22
23. 23. Module 3 Lesson 12.notebook January 28, 2014 23