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Module 3 Lesson 13 Intro to Inequalities.notebook
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AIM: Properties of Inequalities
Do Now
11/15/16 Homework:Lesson 13 Problem Set Page 55 #1-4
Module 3 Lesson 12
Lesson 12 Sprint
Module 3 Lesson 13 Intro to Inequalities.notebook
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Module 3 Lesson 12 Sprint Round 1
Module 3 Lesson 13 Intro to Inequalities.notebook
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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 51
Module 3 Lesson 13 Intro to Inequalities.notebook
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means the inequality symbol stays the same
means the inequality symbol switches direction
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Module 3 Lesson 13 Intro to Inequalities.notebook
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When adding and subtracting, the inequality symbol is preserved
Module 3 Lesson 13 Intro to Inequalities.notebook
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4 3>4 + 3 > 3 + 3 1 > 6 Preserved
3 > 23 2 > 2 2 1 > 0 Preserved
3 4> 3 (1) > 4 (1) 2 > 3
2 5< 2 + 1 < 5 + 11 < 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 > -4The 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
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
Station 2
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4 3>
3 > 2
3 4>
2 5<
4(2) > (3)(2) 8 > 6
3 > 22 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
Station 2
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53
When multiplying and dividing by a negative, the inequality symbol is reversed.
Station 3
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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 > 22 2
1.5 < 1
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When multiplying and dividing by a negative, the inequality symbol is reversed.
Station 3
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DiscussionTo 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 < 74(-1) < 7(-1)
-4 > -7
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Preserved
Reversed
PreservedPreserved
PreservedReversed
PreservedPreserved
ReversedPreserved
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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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