Writing & Graphing Writing & Graphing InequalitiesInequalities

Learning Objective: Learning Objective: To write and To write and graph inequalities on the number line graph inequalities on the number line

because I want to be able to because I want to be able to represent situations that have more represent situations that have more

than one correct answer.than one correct answer.

EQ: EQ: How can I write, How can I write, interpret and represent interpret and represent

inequalities?inequalities?

Where might I see Where might I see inequalities in real life?inequalities in real life?

If it’s any smaller, you’ve got to If it’s any smaller, you’ve got to throw him back!throw him back!

OpeningOpening

4 ft. tall and taller

Explain all the possible heights to ride the Dragon Coaster in feet.

x > 4 ft.

See if you can figure out how to represent this with an inequality symbol and a variable.

What are the possible solutions for x (the variable)?

4’, 4’1”, 4’2” . . . 6’, 6’1”, etc.! And everythingin between!

What are some other What are some other situations that have more situations that have more

than one answer or than one answer or qualifying response?qualifying response?

Examples: Scores that qualify for an A: > 90 Money you need to get into Six Flags: > $39 Age required to get the kids’ meal: < 10 years old) Number of days to complete your project < 5 days

Writing and Graphing Writing and Graphing InequalitiesInequalities

Dr. Burger helps us write inequalities

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

And:And:

≠

Symbol Meaning Word Phrases

is not equal to Is not equal to

Write an inequality for each situation.

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

number of people ≥ 15 or x ≥ 15

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

number of people ≤ 60 or x ≤ 60

“At least” means greaterthan or equal to. Solution Set?

“No more than” meansless than or equal to.Solution set?

Write an inequality for each situation.

Check It Out: Example 1

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

gallons of gas ≤ 10 or x ≤ 10

D. There are at least 10 yards of fabric left.

yards of fabric ≥ 10 or x ≥ 10

“At most” means lessthan or equal to. SOLUTION set?.

“At least” meansgreater than or equal to.Solution set?

Course 2

12-4 Inequalities

Graphing InequalitiesGraphing Inequalities

Words aren’t enough. I want to show Words aren’t enough. I want to show an inequality on a number line. Can I an inequality on a number line. Can I do that??do that??

Dr. Burger says yes! We can graph inequalities

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

To indicate that solutions include numbers with values less than the point graphed, shade to the left of the point.

To show that solutions include numbers greater than the point graphed, shade to the right of the point.

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

On your own paper, graph each inequality.

Additional Example 2: Graphing Simple Inequalities

–2 –1 0 1 2 3

A. n < 33 is not a solution, so draw an open circle at 3. Shade the line to the left of 3.

B. a ≥ –4

–6 –4 –2 0 2 4 6

–4 is a solution, so draw a closed circleat –4. Shade the lineto the right of –4.

Course 2

12-4 Inequalities

On your own paper, graph each inequality.

Check It Out: Example 2

–3 –2 –1 0 1 2 3

A. p ≤ 22 is a solution, so draw a closed circle at 2. Shade the line to the left of 2.

B. e > –2

–3 –2 –1 0 1 2 3

–2 is not a solution, so draw an open circleat –2. Shade the lineto the right of –2.

Course 2

12-4 Inequalities

Lesson Quiz: Part II

Graph the inequalities on your own paper.

1. x > –1

Insert Lesson Title Here

0º

1 2 3123 – – –

2. x < –1

0º

1 2 3123 – – –

Course 2

12-4 Inequalities

Lesson Quiz: Part II

Graph the inequalities, continued.

3. x > –1

Insert Lesson Title Here

0º

1 2 3123 – – –

4. x < –1

0º

1 2 3123 – – –

Course 2

12-4 Inequalities

How did you do?!Temperature Check!

Give me a thumbs up if you did a great job and didn’t miss any

Give me a sideways thumb if you did alright, but you probably need to work on it a little bit

Give me a thumbs down if you aren’t getting it yet, and you need some help

Let’s get wordy!

Who remembers some key words and phrases that tell us which inequality sign to choose? Raise your hand!

Now let’s make our own review flip books!

Let’s begin by taking the 4 pieces of paper you were given and stacking them with about a 1-2 inch overlap

Now hold the papers together and fold the top down so you have eight 1-2 inch flaps, and put two staples at the very top to hold your flip book together.

Write “Inequalities” on the top flap

Copy the following graphs onto each new flap on your flip book as they are shown to you. Make sure that you pay attention whether the circles are open or closed!

Now that we’ve completed the graphs for our flip books, let’s begin writing the inequalities that each graph represents. Make sure that you can write the inequality with the variable both on the right AND the left of the inequality sign. What happens when you switch the side that the inequality is on?

Now we will use these key words to write some word problems for our inequality graphs. Look at the example below to see what I mean…

Are you pickin up what I’m puttin down?

Let’s finish up by writing word problems for the rest of the graphs. Try to do them on your own, and have your elbow partner check when you’ve finished.

Write about what you’ve learned:Write about what you’ve learned:Complete Reading Strategies

1.1. Use complete sentences.Use complete sentences.

2.2. Turn it over on your desk when done. It will be Turn it over on your desk when done. It will be collected.collected.

3.3. Make sure your name, date, class period are on it!Make sure your name, date, class period are on it!