Lesson 4.1 Inequalities and Their Graphs.notebook
October 31, 2011
4.1 Inequalities and their Graphs!!
Objectives:
• Be able to identify solutions to inequalities
• Be able to write and graph inequalities WARM UP
Complete each statement with <, >, or =
1) ­3 __ ­5
2) 4.29 ___ 4.8
3) (­3)(­4) ___ 12
4) ­1 ­ 2 ___ 6 ­ 9
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Lesson 4.1 Inequalities and Their Graphs.notebook
October 31, 2011
Some Background Info:
An equation uses what symbol???
An inequality will use these symbols:
< means ­­­_____________
> means _____________
≤
means ______________________
≥ means _____________________
Write how you would say these expressions in words:
x < 5 x
is less than 5
x > ­11 x
is greater than -11
x ≥ 6 x
is greater than or equal to 6
x ≤ 0 x
is less than or equal to 0
2
Lesson 4.1 Inequalities and Their Graphs.notebook
October 31, 2011
Solution: Any number that makes the inequality true
what are possible solutions of the inequality x ≤ 7?
x < 3
m ≥ ­2
­1 ≥ a
3
Lesson 4.1 Inequalities and Their Graphs.notebook
October 31, 2011
­2 > c
4 ≤ n
a ≤ 0
is 3 a solution of the inequality 2 ­ 5x > 13?
4
Lesson 4.1 Inequalities and Their Graphs.notebook
October 31, 2011
Is each number a solution to the inequality 6x ­ 3 > 10?
a) 1
­10
­10
­10
­10
­9
­9
­8
­8
­6
­7
­8
­9
­6
­7
­8
­9
­7
­7
­6
­6
­5 ­4
­5 ­4
­3
­3
­2
­2
­1
­1
1
0
0
2
1
0
­1
­2
­3
1
0
­1
­2
­3
­5 ­4
­5 ­4
d) 4
c) 3
b) 2
2
2
1
3
3
3
2
4
4
4
3
5
5
5
4
6
6
6
5
8
7
10
9
10
9
8
10
9
8
7
7
6
8
7
9
10
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Lesson 4.1 Inequalities and Their Graphs.notebook
October 31, 2011
Define a variable. Write an inequality. Graph your inequality.
1.) The temperature today will be at least 62 degrees.
2.) Rachel has to baby sit today. She will make at most $25.
3.) Your dinner at Texas Roadhouse will cost you more than twelve dollars.
4.) You can have no more than 15 people on your dogeball team.
Graph: Open circle
0
6
Graph: Closed circle
Example:
Example:
x < 6
or
6 > x
­2 < x
"x is greater than "x is less than six" negative two"
Example:
Example:
or
3 ≥ x 3
x > ­2
or
x ≤ 3
0
Graph:Open circle
0
­2
Graph: Closed circle
x ≥ 1
or
1 ≤ x
"x is less than or "x is greater than equal to three"
or equal to one"
0
1
6
Lesson 4.1 Inequalities and Their Graphs.notebook
October 31, 2011
Solve each inequality. Check your answer, then graph your solution
1.) m - 6 > -4
3.) y + 5 < -7
2.) n - 7 ≤ -2
4.) t + 3 ≥ 8
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