GRAB YOUR NOTEBOOK AND LABEL THE NEXT BLANK PAGE UNIT 16.(If you have no room in your notebook, do the warm-up and notes on a piece of paper in a binder or folder)

Warm UpSolve.

1.–21 + 12z = –27

2. –18 = –6n

3. 56 + x = 8

4. 9k - 9 = –18

n = 3

x = -48

Course 2

12-4 Inequalities

k = -1

Learn to read and write inequalities and graph them on a number line.

Course 2

12-4 Inequalities

Homework: Kuta worksheet

An inequality states that two quantitieseither are not equal or may not be equal. An inequality uses one of the following symbols:

Symbol Meaning Word Phrases

<

>

≤

≥

is less than

is greater than

is greater than or equal to

is less than or equal to

Fewer than, below

More than, above

At most, no more than

At least, no less than

Course 2

12-4 Inequalities

Write an inequality for each situation.

Additional Example 1: Writing Inequalities

A. There are at least 15 people in the waiting room.

number of people ≥ 15

B. The tram attendant will allow no more than 60 people on the tram.

number of people ≤ 60

Course 2

12-4 Inequalities

Write an inequality for each situation.

Check It Out: Example 1

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

gallons of gas ≤ 10

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

yards of fabric ≥ 10

Course 2

12-4 Inequalities

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.

Course 2

12-4 Inequalities

This open circle shows that 5 is not a solution.

a > 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

Course 2

12-4 Inequalities

Graph each inequality.

Additional Example 2: Graphing Simple Inequalities

–3 –2 –1 0 1 2 3

A. n < 3

B. a ≥ –4

–6 –4 –2 0 2 4 6

Course 2

12-4 Inequalities

Graph each inequality.

Check It Out: Example 2

–3 –2 –1 0 1 2 3

A. p ≤ 2

B. e > –2

–3 –2 –1 0 1 2 3

Course 2

12-4 Inequalities

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.

number of eggs ≥ 12

people in the theater ≤ 220

Insert Lesson Title Here

people attending the meeting < 14

Course 2

12-4 Inequalities

Lesson Quiz: Part II

Graph the inequalities.

4. x > –1

Insert Lesson Title Here

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1 3 5123 – – –

Course 2

12-4 Inequalities