Chapter 22-1 Graphing Inequalities

ObjectivesThe students will learn to:Identify solutions of inequalities in one

variableWrite and graph inequalities in one variable

What is an inequality ?An inequality is a statement that two

quantities are not equal. The quantities are compared by using the following signs:

≤A ≤ B

A is less than or

equal to B.

<A < B

A is lessthan B.

>A > B

A is greaterthan B.

≥A ≥ B

A is greaterthan or

equal to B.

≠A ≠ B

A is notequal to B.

What is a solution to an Inequality?Answer: A solution of an inequality is any value of

the variable that makes the inequality true.

Identifying Solutions of inequalitiesExample #1Describe the solutions of x – 6 ≥ 4 in

wordsx -3 0 9.9 10 10.1 12

X-6 -9 -6 3.9 4 4.1 6

x – 6 ≥ 4

–9 ≥ 4

–6 ≥ 4

3.9 ≥ 4

4 ≥ 4 4.1 ≥ 4

6 ≥ 4

Solution?

No NO NO Yes Yes Yes

Example #1 solutionWhen the value of x is a number less than

10, the value of x – 6 is less than 4. When the value of x is 10, the value of x –

6 is equal to 4.When the value of x is a number greater

than 10, the value of x – 6 is greater than 4.

Solution:It appears that the solutions of x – 6 ≥ 4 are all real numbers greater than or equal to 10.

Example #2Describe the solutions of 2p > 8 in words.

p -3 0 3.9 4 4.1 5

2p -6 0 7.8 8 8.2 10

2p > 8

-6 > 8

0 > 8 7.8 > 8

8 > 8 8.2 > 8

10 > 8

Solution?

No NO NO No Yes Yes

Example #2 solutionWhen the value of p is a number less than

4, the value of 2p is less than 8. When the value of p is 4, the value of 2p is

equal to 8.When the value of p is a number greater

than 4, the value of 2p is greater than 8.Solution: It appears that the solutions of 2p

> 8 are all real numbers greater than 4.

How to graph linear inequalities?How can we graph an inequality like 3 + x < 9 An inequality like 3 + x < 9 has too many

solutions to list. You can use a graph on a number line to show all the solutions.

Solution:

Graph Inequality Graph x > 2Solution:Draw a non-shaded or open circle at 2 and

shade everything on the right of 2. The shaded area in red is your solution. It means that the solution can be any number on the right of 2.Notice that 2 is not shaded because 2 is not included in your solution.

Graph inequalitiesGraph x ≥ 6

Solution:Draw a shaded circle at 6 and then shade everything on the right of 6Notice that this time, the circle is shaded because x is also equal to 6.

Graph inequalitiesGraph x ≤ -1Solution:Draw a shaded circle at -1 and then shade

everything on the left of -1

Graph inequalities22 – 4 ≥ w m ≤ –3

Student Guided practiceWork on problems 1-10 from worksheet

Writing Linear inequalitiesWrite the inequality shown by each graph.

Solution: x < 2

Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2 means that 2 is not a solution, so use <.

Writing linear inequalitiesWrite the inequality shown by each graph.

Student guided practiceGo over writing linear inequalities worksheet problems 3-10

Graphing linear inequalities applicationsRay’s dad told him not to turn on the air

conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions.

Solution: t 85

75 80 85 9070

Application’s example A store’s employees earn at least $8.50

per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.

HomeworkDo problems 22-31 from page 103

ClosureToday we saw about graphing and writing

linear inequalities Next class we are going to learn how to solve

for them

Have a great day!!