This document contains notes from a mathematics lesson on properties of inequalities. It includes examples of how the inequality symbol is preserved or reversed when performing operations like addition, subtraction, multiplication, and division. Specifically: - The inequality symbol is preserved when adding, subtracting, or multiplying/dividing by a positive number. - The inequality symbol is reversed when multiplying or dividing by a negative number. - A greater than symbol becomes a less than symbol, or vice versa, when the inequality is reversed due to multiplying or dividing by a negative number.

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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

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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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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

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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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means the inequality symbol
stays the same
means the inequality symbol
switches direction
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When adding and subtracting, the inequality
symbol is preserved

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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
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When adding and subtracting, the inequality
symbol is preserved

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When multiplying by ­1, the inequality symbol is
reversed

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-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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-3 < 4
-3(-1) < 4(-1)
3 > -4
The symbol is
reversed

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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
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When multiplying by ­1, the inequality symbol is
reversed

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When multiplying or dividing by a positive
value, the inequality symbol is preserved

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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
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When multiplying or dividing by a positive
value, the inequality symbol is preserved

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When multiplying and dividing by a negative,
the inequality symbol is reversed.

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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
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When multiplying and dividing by a negative,
the inequality symbol is reversed.

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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
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4 < 7
4(-1) < 7(-1)
-4 > -7

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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.
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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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