Writing & Graphing Writing & Graphing InequalitiesInequalities

Learning Target: Learning Target: Today I am Today I am learning learning how to write and graph how to write and graph inequalities on the number line inequalities on the number line becausebecause I want to be able to I want to be able to represent situations that have more represent situations that have more than one correct answer.than one correct answer.

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!

OpeningOpening1.1. You are going to Six Flags as soon as school is You are going to Six Flags as soon as school is

out (yaay!). You have to be at least 4 ft. tall to out (yaay!). You have to be at least 4 ft. tall to ride some of your favorite rides, but it isn’t ride some of your favorite rides, but it isn’t only 4-foot tall people who can ride the rides! only 4-foot tall people who can ride the rides! How tall can you be and ride the rides?How tall can you be and ride the rides?

2.2. See if you can figure out how to represent this See if you can figure out how to represent this with an inequality sign and a variable. (Hint: with an inequality sign and a variable. (Hint: if it were an equation it would look like this: x if it were an equation it would look like this: x = 4 ft. Use one of the inequality symbols = 4 ft. Use one of the inequality symbols posted on the board to make it an inequality.)posted on the board to make it an inequality.)

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

4 ft. tall and taller

x > 4 ft.

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

What are some other situations that What are some other situations that have more than one answer or have more 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

An inequality that contains a variable An inequality that contains a variable is an is an algebraic inequalityalgebraic inequality. A value . A value of the variable that makes the of the variable that makes the inequality true is a solution of the inequality true is a solution of the inequality.inequality.An inequality may have more than one solution. Together, all of the solutions are called the solution set..

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.

“No more than” meansless than or equal to.

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.

“At least” meansgreater than or equal to.

Course 2

12-4 Inequalities

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!

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

Symbols ReviewSymbols Review

Open CircleOpen Circle The number is The number is not not

includedincluded in the in the solution.solution.

Closed CircleClosed Circle The number The number is is

includedincluded in the in the solution.solution.

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.

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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.

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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

Now let’s make our own review flip books!

Let’s begin by taking the 3 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 six 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 go through each graph and fill in the inequalities. When you have finished, check with a partner close to you.

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 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.