Module 3 lesson 12

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

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

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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

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

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January 19, 2016
means the inequality symbol
stays the same
means the inequality symbol
switches direction
S.69

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January 19, 2016
S.69
When adding and subtracting, the inequality
symbol is preserved

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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

8
January 19, 2016
S.70
When multiplying by 1, the inequality symbol is
reversed

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?

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January 19, 2016
-3 < 4
-3(-1) < 4(-1)
3 > -4
The symbol is
reversed

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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

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January 19, 2016
S.71
When multiplying or dividing by a positive
value, the inequality symbol is preserved

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

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January 19, 2016
S.72
When multiplying and dividing by a negative,
the inequality symbol is reversed.

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.

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

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January 19, 2016
4 < 7
4(-1) < 7(-1)
-4 > -7

18
January 19, 2016
S.73

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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

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

Module 3 lesson 12

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Module 3 lesson 12