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Module 3 lesson 12

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Erik Tjersland
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Module 3 Lesson 12.notebook 1 January 16, 2015 AIM: Properties of Inequalities Do Now 1/16/15 Homework: Problem Set 12 #1-3Module 3 Lesson 12 Lesson 12 Sprint
Module 3 Lesson 12.notebook 2 January 16, 2015 4 3 2 1 0 ­1 ­2 7 9 11 13 15 5 4 2 0 ­1 ­2 ­3 ­6 ­18 ­6 35 35 35 35 35 4 4 4 4 4 7 5 3 1 ­1 ­3 ­1 ­1 ­1 5 ­1 ­5 Module 3 Lesson 12 Sprint Round 1
Module 3 Lesson 12.notebook 3 January 16, 2015 2 3 4 5 6 7 8 10 12 14 16 20 3 2 1 0 ­1 ­3 ­4 ­8 ­12 ­4 50 50 50 50 50 4 4 4 4 4 ­1/2 ­3/2 ­7/2 ­4 ­9/2 1 1 1 1 ­5/2 2 ­1 Module 3 Lesson 12 Sprint Round 2
Module 3 Lesson 12.notebook 4 January 16, 2015 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 Inequalities
Module 3 Lesson 12.notebook 5 January 16, 2015 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 S.69
Module 3 Lesson 12.notebook 6 January 16, 2015 S.69
Module 3 Lesson 12.notebook 7 January 16, 2015 4 ­3> 4 + ­3 > ­3 + ­3        1 > ­6 Preserved 3 > 2 3 ­ 2 > 2 ­ 2      1 > 0 Preserved ­3 ­4> ­3 ­ (­1) > ­4 ­ (­1)          ­2 > ­3 ­2 5< ­2 + 1 < 5 + 1 ­1 < 6 Preserved Preserved S.69
Module 3 Lesson 12.notebook 8 January 16, 2015 S.70
Module 3 Lesson 12.notebook 9 January 16, 2015 -3 < 4 -3(-1) < 4(-1) Plot the points on the number line below based on multiplying both values by -1. What is the result to the inequality symbol?
Module 3 Lesson 12.notebook 10 January 16, 2015 -3 < 4 -3(-1) < 4(-1) 3 > -4 The symbol is reversed
Module 3 Lesson 12.notebook 11 January 16, 2015 4 ­3> 3 > 2 ­3 ­4> ­2 5< 4(­1) > (­3)(­1)    ­4 < 3 Reversed Reversed Reversed 3(­1) > 2(­1)    ­3 < ­2 ­3(­1) > (­4)(­1)        3 < 4 ­2(­1) < 5(­1)        2 > ­5 Reversed S.70
Module 3 Lesson 12.notebook 12 January 16, 2015 S.71
Module 3 Lesson 12.notebook 13 January 16, 2015 4 ­3> 3 > 2 ­3 ­4> ­2 5< 4(2) > (­3)(2)    8 > ­6 3 > 2 2    2    1.5 > 1 ­3 > (­4)         ­6 > ­8 ­2(3) < 5(3)       ­6 < 15 Preserved Preserved Preserved Preserved S.71
Module 3 Lesson 12.notebook 14 January 16, 2015 S.72
Module 3 Lesson 12.notebook 15 January 16, 2015 4 ­3> 3 > 2 ­3 ­4> ­2 5< 4(­3) > (­3)(­3)    ­12 < 9 ­3 > (­4)        6 < 8 ­2(   ) < 5(   )        1 > ­2.5 Reversed Reversed Reversed Reversed 3 > 2 ­2   ­2    ­1.5 < ­1 S.72
Module 3 Lesson 12.notebook 16 January 16, 2015 Discussion To summarize, when did the inequality symbol  change and when did it stay the same? Preserved Reversed 1.) Add or subtract any number 2.) Multiply or divide by a positive 1.) Multiply or divide by a negative S.73
Module 3 Lesson 12.notebook 17 January 16, 2015 4 < 7 4(-1) < 7(-1) -4 > -7
Module 3 Lesson 12.notebook 18 January 16, 2015 S.73
Module 3 Lesson 12.notebook 19 January 16, 2015 2 + 1 < 5 + 1       3 < 6 2(­1) < 5(­1)      ­2 > ­5 Multiplying by a  negative reverses  the symbol. ­4 ­ 1 > ­6 ­ 1       ­5 > ­7 ­4 > ­6 ­2    ­2       2 < 3 Dividing by a  negative reverses  the symbol. ­1(6)    2(6)     ­6    12 ­1(­4)    2(­4)       4    ­8 Multiplying by a  negative reverses  the symbol. ­5 + 5 < ­4 + 5       0 < 1 ­5 < ­4        ­5 < ­4 ­1    ­1       5 > 4 Dividing by a  negative reverses  the symbol. S.73
Module 3 Lesson 12.notebook 20 January 16, 2015 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? S.74

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Module 3 lesson 12