Lesson 4.1 Inequalities and Their Graphs.notebook
November 01, 2011
Chapter 4: Solving Inequalities
Objectives:
• Be able to identify solutions to inequalities
• Be able to write and graph inequalities Nov 1­1:15 PM
4.1 Inequalities and their Graphs!!
Oct 13­5:16 PM
1
Lesson 4.1 Inequalities and Their Graphs.notebook
November 01, 2011
WARM UP
Complete each statement with <, >, or =
1) ­3 __ ­5
2) 4.29 ___ 4.8
3) (­3)(­4) ___ 12
4) ­1 ­ 2 ___ 6 ­ 9
Nov 29­9:21 PM
Some Background Info:
An equation uses what symbol???
An inequality will use these symbols:
< means ­­­_____________
> means _____________
≤
means ______________________
≥ means _____________________
Nov 29­9:26 PM
2
Lesson 4.1 Inequalities and Their Graphs.notebook
November 01, 2011
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
Nov 29­9:30 PM
Solution: Any number that makes the inequality true
what are possible solutions of the inequality x ≤ 7?
Nov 29­9:38 PM
3
Lesson 4.1 Inequalities and Their Graphs.notebook
November 01, 2011
x < 3
m ≥ ­2
­1 ≥ a
Nov 29­9:49 PM
­2 > c
4 ≤ n
a ≤ 0
Nov 29­9:49 PM
4
Lesson 4.1 Inequalities and Their Graphs.notebook
November 01, 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.
Oct 31­10:21 AM
is 3 a solution of the inequality 2 ­ 5x > 13?
Nov 2­6:19 PM
5
Lesson 4.1 Inequalities and Their Graphs.notebook
November 01, 2011
Is each number a solution to the inequality 6x ­ 3 > 10?
d) 4
c) 3
b) 2
a) 1
Nov 2­6:19 PM
­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
0
0
2
1
0
­1
­2
­3
­5 ­4
1
0
­1
­2
­3
­5 ­4
1
1
3
2
2
2
3
3
3
4
5
4
4
4
5
5
5
6
6
6
6
8
7
8
7
7
7
8
8
10
9
10
9
9
9
10
10
Nov 29­9:55 PM
6
Lesson 4.1 Inequalities and Their Graphs.notebook
Graph: Open circle
Example:
x < 6
Graph: Closed circle
x > ­2
or
or
6 > x
­2 < x
Example:
Example:
Graph: Closed circle
or
or
3 ≥ x 3
0
­2
x ≥ 1
x ≤ 3
0
Graph:Open circle
"x is greater than negative two"
"x is less than six"
6
0
Example:
November 01, 2011
1 ≤ x
"x is less than or "x is greater than equal to three"
or equal to one"
0
1
Nov 29­10:03 PM
Homework #21
Pg 202 #11, 13, 15­18, 19, 21, 23, 24,
27­30, 33­41
Oct 21­5:20 PM
7
Lesson 4.1 Inequalities and Their Graphs.notebook
November 01, 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
Nov 29­10:06 PM
8