1. What do you do when things are not equal???
Linear Inequalities

2. Linear Inequalities
The reality in life, is that things do not always work out equally.
In math, we need to be able to represent this inequality
We can represent this verbally (by using words), graphically(by using pictures) and algebraically (with mathematical symbols)

3. Linear Inequalities - let’s begin
Have you ever seen one of those signs at the Ex that says you have to be a certain height to go on the ride?
well… that sign represents an inequality: there is not a single, correct answer, is there?
An inequality has a range of numbers that are a possible answer.

4. representing inequalities
Did you know that the NHL has limits for the equipment that the players can use?
For example, no hockey stick can exceed 160 cm in length.
This means that there is a variety of lengths possible.

5. representing inequalities
How can you represent this statement:
Verbally?
“A hockey stick must be less than or equal to 160 cm in length”
Graphically?
Algebraically?

6. representing inequalities
When you algebraically represent an inequality, there is no “equals” sign. It is not possible to have one, single , correct answer.
Possible symbols to use include:
Less than
Greater than
Less then or equal to
Greater than or equal to
Is not equal to

7. representing inequalities
When you use a number line to graphically represent an inequality, you must pay particular attention to the boundary point on your solution.
A closed circle shows that the boundary point IS included in your answer.
An open circle shows that the boundary point IS NOT included in your answer.

8. representing inequalities
Here’s a typical problem:
Reesa works at the virology lab. She earns overtime when she works more than 40 hours a week.
Verbally express the amount of time that qualifies for overtime
“Reesa must work more than 40 hours a week to qualify for overtime”
Create a number line to graphically express the amount of time that qualifies for overtime
Express the inequality algebraically (let t represent time)

9. representing inequalities
Sometimes you can have a combination of inequalities
This statement describes two inequalities at once: “The average person listens to at least 3 hours of music a day, but less than 5 hours.”
Graphically:
Algebraically:

10. Practice, practice, practice
Practice the basic skills on these questions:
Page 347: #5, 6, 7, 8,
9 (with word statement and algebraically) 11,13, 15
Apply the basics with these word problems:
Page 348 #16, 17, 18, 20, 22