Warm Up

Problem of the Day

Lesson Presentation

Warm Up Solve. 1. 21z 12 27z 2. 12n 18

6n 3. 12y 56 8y 4. 36k 9 18k

z 2

n 3

y 14

1 2

k

Problem of the Day The dimensions of one

rectangle are twice as large as the dimensions of

another rectangle. The difference in area is 42

cm2. What is the area of each rectangle?

56 cm2 and 14 cm2

Learn to read and write inequalities and graph

them on a number line.

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Vocabulary

inequality algebraic inequality solution

set compound inequality

An inequality states that two quantities either

are not equal or may not be equal. An inequality

uses one of the following symbols

Symbol Meaning Word Phrases

lt

gt

is less than

Fewer than, below

is greater than

More than, above

is less than or equal to

At most, no more than

is greater than or equal to

At least, no less than

Additional Example 1 Writing Inequalities

Write an inequality for each situation.

A. There are at least 15 people in the waiting

room.

At least means greater than or equal to.

number of people 15

B. The tram attendant will allow no more

than 60 people on the tram.

No more than means less than or equal to.

number of people 60

Check It Out Example 1

Write an inequality for each situation.

A. There are at most 10 gallons of gas in the

tank.

At most means less than or equal to.

gallons of gas 10

B. There is at least 10 yards of fabric left.

At least means greater than or equal to.

yards of fabric 10

An inequality that contains a variable is an

algebraic inequality. A value of the variable

that makes the inequality true is a solution of

the inequality.

An inequality may have more than one solution.

Together, all of the solutions are called the

solution set.

You can graph the solutions of an inequality on a

number line. If the variable is greater than or

less than a number, then that number is

indicated with an open circle.

This open circle shows that 5 is not a solution.

a gt 5

If the variable is greater than or equal to or

less than or equal to a number, that number is

indicated with a closed circle.

This closed circle shows that 3 is a solution.

b 3

Additional Example 2 Graphing Simple Inequalities

Graph each inequality.

A. n lt 3

3 is not a solution, so draw an open circle at

3. Shade the line to the left of 3.

3 2 1 0 1 2 3

B. a 4

4 is a solution, so draw a closed circle at 4.

Shade the line to the right of 4.

6 4 2 0 2 4 6

Check It Out Example 2

Graph each inequality.

A. p 2

2 is a solution, so draw a closed circle at 2.

Shade the line to the left of 2.

3 2 1 0 1 2 3

B. e gt 2

2 is not a solution, so draw an open circle at

2. Shade the line to the right of 2.

3 2 1 0 1 2 3

A compound inequality is the result of combining

two inequalities. The words and and or are used

to describe how the two parts are related.

x gt 3 or x lt 1

2 lt y and y lt 4

x is either greater than 3 or less than1.

y is both greater than 2 and less than 4. y

is between 2 and 4.

Additional Example 3A Graphing Compound

Inequalities

Graph each compound inequality.

m 2 or m gt 1

First graph each inequality separately.

m 2

m gt 1

º

Then combine the graphs.

The solutions of m 2 or m gt 1 are the combined

solutions of m 2 or m gt 1.

Additional Example 3B Graphing Compound

Inequalities

Graph each compound inequality

3 lt b 0

3 lt b 0 can be written as the inequalities 3

lt b and b 0. Graph each inequality separately.

3 lt b

b 0

º

Then combine the graphs. Remember that

3 lt b 0 means that b is between 3 and 0,

and includes 0.

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Check It Out Example 3A

Graph each compound inequality.

w lt 2 or w 4

First graph each inequality separately.

w lt 2

W 4

Then combine the graphs.

The solutions of w lt 2 or w 4 are the combined

solutions of w lt 2 or w 4.

Check It Out Example 3B

Graph each compound inequality

5 gt g 3

5 gt g 3 can be written as the inequalities 5 gt

g and g 3. Graph each inequality separately.

5 gt g

g 3

º

Then combine the graphs. Remember that

5 gt g 3 means that g is between 5 and 3,

and includes 3.

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Lesson Quiz Part I

Write an inequality for each situation. 1. No

more than 220 people are in the theater. 2.

There are at least a dozen eggs left. 3. Fewer

than 14 people attended the meeting.

people in the theater 220

number of eggs 12

people attending the meeting lt 14

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Lesson Quiz Part II

Graph the inequalities. 4. x gt 1

5. x 4 or x lt 1