An inequality is a mathematical sentence that contains <, >, ≤, or ≥
What do each of these symbols mean?
<
>
≤
≥
1
Write an inequality to represent each sentence:
Your age is less than 6 years
Your height is greater than 40 inches.
Your speed is less than or equal to 35 miles per hour
Your speed is greater than or equal to 55 miles per
hour.
2
A food can be labeled low fat only if it has no more than 3 grams per serving. Write an inequality to describe low fat foods.
To meet a certain air quality standard, an automobile must have a fuel efficiency of not less than 27.5 miles per gallon. Write an inequality to describe this situation.
3
Write an inequality for each of these sentences. Then compare with your neighbor:
Your age is less than 19 years.
Your height is greater than 52 inches
Your speed is no more than 65 miles per hour.
You speed is at least 70 miles per hour
4
If an inequality has a variable in it, then it is an open sentence. We can determine if an inequality is true or false for a given number if we replace the variable with the number.
For the given value, state whether each inequality is true or false:
s ­ 7 < 7, s = 14
12≥ a + 2, a = 20
2 5
State whether the inequality is true or false for each given value
(1 finger for true, 2 for false):
s - 9 < 4, s = 6
14 ≤ a + 1, a = 36
3
6
Graphing inequalities:
Since an inequality like x > 4 represents many possibilities for x, we can show these all on a number line:
­10
­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
2
3
4
5
6
7
8
9
10
7
If the inequality is eating the variable, then shade to the right. Why?
> : open circle
<: open circle
If the inequality is eating the number, then shade to the left.
Why?
≥: closed circle
≤: closed circle
Graph:
x < 4
x > 4
­10 ­9
­8 ­7 ­6
­5 ­4 ­3 ­2 ­1
0
1
2
3
4
5
6
7
8
9
10
­10 ­9
­8 ­7 ­6
­8 ­7 ­6
0
1
1
2
2
3
4
4
5
5
6
7
8
9
7
8
9
10
10
x ≤ 4
x≥4
­10 ­9
­5 ­4 ­3 ­2 ­1
­5 ­4 ­3 ­2 ­1
0
1
2
3
4
5
6
7
8
9
10
­10 ­9
­8 ­7 ­6
­5 ­4 ­3 ­2 ­1
0
3
6
8
Write the inequality for the graph:
­10
­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
2
3
4
5
6
7
8
9
10
9
Whiteboards:
Write an inequality for each sentence:
A number increased by 14 is at least 25.
Five times some number is less than 65.
10
For the given value, state whether the inequality is true or false:
n + 4 > 6, n = 12
34≤ 4r, r = 8
11
Graph each inequality on a number line:
n > 3
­10
­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
2
3
5
4
6
7
8
9
10
5 ≥p
­10
­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
2
1
10
9
8
7
6
5
4
3
x < 7
­10
­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
2
3
4
5
6
7
8
9
10
12
Write the inequality for each graph:
­10
­10
­9
­9
­8
­8
­7
­7
­6
­6
­5 ­4
­5 ­4
­3
­3
­2
­2
­1
­1
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
13
The elevators in an office building have been approved for a maximum load of 3600 pounds. Write an inequality to describe a safe load.
14