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
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2. Module 3 Lesson 12.notebook
January 28, 2014
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3. Module 3 Lesson 12.notebook
January 28, 2014
Exit Ticket Solution:
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4. Module 3 Lesson 12.notebook
January 28, 2014
Homework Answers
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5. Module 3 Lesson 12.notebook
January 28, 2014
Homework Answers
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6. Module 3 Lesson 12.notebook
January 28, 2014
Homework Answers
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7. Module 3 Lesson 12.notebook
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Opening Exercise
Sprint
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8. Module 3 Lesson 12.notebook
January 28, 2014
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9. Module 3 Lesson 12.notebook
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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
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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
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12. Module 3 Lesson 12.notebook
January 28, 2014
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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
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14. Module 3 Lesson 12.notebook
January 28, 2014
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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
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16. Module 3 Lesson 12.notebook
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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
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18. Module 3 Lesson 12.notebook
January 28, 2014
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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
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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
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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.
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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?
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23. Module 3 Lesson 12.notebook
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