# Integers

Writing & Graphing Inequalities Learning Objective: To write and graph inequalities on the number line because I want to be able to represent situations that have more than one correct answer. Where might I see inequalities in real life?

If its any smaller, youve got to throw him back! Opening 1. 2. You are going to Six Flags as soon as school is

out (yaay!). You have to be at least 4 ft. tall to ride some of your favorite rides, but it isnt only 4-foot tall people who can ride the rides! How tall can you be and 4 ft.ride tallthe andrides? taller See if you can figure out how to represent this with an inequality sign and a variable. (Hint: if it were an equation it would look like this: x

= 4 ft. Use one of the inequality symbols posted on the board to make it an inequality.) x > 4 ft. What are the possible solutions for x (the 4,variable)? 41, 42 . . . 6, 61, etc.! And everything in between! 3.

What are some other situations that have more than one answer or 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 Inequalities Dr. Burger helps us write inequalities 12-4 Inequalities An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols: Symbol

< > Course 2 Meaning Word Phrases is less than

Fewer than, below is greater than is less than or equal to More than, above is greater than or equal to

At least, no less than At most, no more than And: Symbol Meaning is not equal to

Word Phrases Is not equal to 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. Write an inequality for each situation. A. There are at least 15 people in the waiting room. number of people 15 or At least means greater than or equal to. x 15 B. The tram attendant will allow no more than 60 people on the tram. No more than means

number of people 60 or less than or equal to. x 60 12-4 Inequalities Check It Out: Example 1 Write an inequality for each situation. C. There are at most 10 gallons of gas in the tank. gallons of gas 10 or x 10

At most means less than or equal to. D. There are at least 10 yards of fabric left. yards of fabric 10 or x 10 Course 2 At least means

greater than or equal to. Write about what youve learned: Complete Reading Strategies 1. 2. 3. Use complete sentences.

Turn it over on your desk when done. It will be collected. Make sure your name, date, class period are on it! Graphing Inequalities Words arent enough. I want to show an inequality on a number line. Can I do that?? Dr. Burger says yes! We can graph ine qualities

12-4 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. 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. 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. b3 Course 2 12-4 Inequalities Additional Example 2: Graphing Simple Inequalities On your own paper, graph each inequality. A. n < 3

2 1 0 1 2 3

B. a 4 6 4 Course 2 2 0 2

4 6 3 is not a solution, so draw an open circle at 3. Shade the line to the left of 3. 4 is a solution, so draw a closed circle

at 4. Shade the line to the right of 4. 12-4 Inequalities Check It Out: Example 2 On your own paper, graph each inequality. A. p 2 3 2

1 0 1 2 3 B. e > 2

3 Course 2 2 1 0 1

2 3 2 is a solution, so draw a closed circle at 2. Shade the line to the left of 2. 2 is not a solution, so draw an open circle

at 2. Shade the line to the right of 2. 12-4 Inequalities Insert Lesson Title Here Lesson Quiz: Part II Graph the inequalities on your own paper. 1. x > 1

3 2 1 0 1 2 3

0 1 2 3 2. x < 1

3 2 1 Course 2 12-4 Inequalities Insert Lesson Title Here Lesson Quiz: Part II Graph the inequalities, continued. 3. x > 1

3 2 1 0 1 2

3 0 1 2 3 4. x < 1

3 2 1 Course 2 Now lets make our own review flip books! Lets 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 weve completed the graphs for our flip books, lets 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 didnt 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 arent getting it yet, and you need some help Lets 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 Im puttin down? Lets 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 youve finished.

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