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Module 3 lesson 12

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Module 3 Lesson 12.notebook 1 January 19, 2016 AIM: Properties of Inequalities Do Now 1/19/16 Homework: Problem Set 12 #1-3Module 3 Lesson 12 Lesson 12 Sprint CRS #9 due Thursday  1/21
Module 3 Lesson 12.notebook 2 January 19, 2016 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 19, 2016 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 19, 2016 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 19, 2016 means the inequality symbol  stays the same means the inequality symbol  switches direction S.69
Module 3 Lesson 12.notebook 6 January 19, 2016 S.69 When adding and subtracting, the inequality  symbol is preserved
Module 3 Lesson 12.notebook 7 January 19, 2016 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 When adding and subtracting, the inequality  symbol is preserved
Module 3 Lesson 12.notebook 8 January 19, 2016 S.70 When multiplying by ­1, the inequality symbol is   reversed 
Module 3 Lesson 12.notebook 9 January 19, 2016 -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 19, 2016 -3 < 4 -3(-1) < 4(-1) 3 > -4 The symbol is reversed
Module 3 Lesson 12.notebook 11 January 19, 2016 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 When multiplying by ­1, the inequality symbol is   reversed 
Module 3 Lesson 12.notebook 12 January 19, 2016 S.71 When multiplying or dividing by a positive  value, the inequality symbol is preserved
Module 3 Lesson 12.notebook 13 January 19, 2016 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 When multiplying or dividing by a positive  value, the inequality symbol is preserved
Module 3 Lesson 12.notebook 14 January 19, 2016 S.72 When multiplying and dividing by a negative,  the inequality symbol is reversed.
Module 3 Lesson 12.notebook 15 January 19, 2016 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 When multiplying and dividing by a negative,  the inequality symbol is reversed.
Module 3 Lesson 12.notebook 16 January 19, 2016 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 19, 2016 4 < 7 4(-1) < 7(-1) -4 > -7
Module 3 Lesson 12.notebook 18 January 19, 2016 S.73
Module 3 Lesson 12.notebook 19 January 19, 2016 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 19, 2016 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