Presentation on theme: "Copy in Agenda and TOC Turn in your homework equation sheet."— Presentation transcript:
1 Copy in Agenda and TOC Turn in your homework equation sheet. Complete the warm-up quiz and turn in#8 1/30/13 Writing Inequalities (HOMEWORK)
2 Writing & Graphing Inequalities Learning Target: Today I am learning how 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.
7 If it’s any smaller, you’ve got to throw him back!
8 OpeningYou 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 isn’t only 4-foot tall people who can ride the rides! How tall can you be and ride the rides?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.)What are the possible solutions for x (the variable)?4 ft. tall and tallerx > 4 ft.4’, 4’1”, 4’2” ’, 6’1”, etc.! And everythingin between!
9 What are some other situations that have more than one answer or qualifying response? Examples:Scores that qualify for an A: > 90Money you need to get into Six Flags: > $39Age required to get the kids’ meal: < 10 years old)Number of days to complete your project < 5 days
10 Writing and Graphing Inequalities Dr. Burger helps us write inequalities
11 Inequalities 12-4 An inequality states that two quantities Course 212-4InequalitiesAn inequality states that two quantitieseither are not equal or may not beequal. An inequality uses one of thefollowing symbols:SymbolMeaningWord Phrases<>≤≥is less thanFewer than, belowis greater thanMore than, aboveis less than or equal toAt most, no more thanis greater than or equal toAt least, no less than
12 And:SymbolMeaningWord Phrases≠is not equal toIs not equal to
13 An inequality that contains a variable is an algebraic inequality 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.
14 Write an inequality for each situation. A. There are at least 15 people in the waiting room.“At least” means greaterthan or equal to.number of people ≥ 15 orx ≥ 15B. The tram attendant will allow no morethan 60 people on the tram.“No more than” meansless than or equal to.number of people ≤ 60 orx ≤ 60
15 Inequalities 12-4 Check It Out: Example 1 Course 212-4InequalitiesCheck It Out: Example 1Write an inequality for each situation.C. There are at most 10 gallons of gas in the tank.“At most” means lessthan or equal to.gallons of gas ≤ 10 orx ≤ 10D. There are at least 10 yards of fabric left.“At least” meansgreater than or equal to.yards of fabric ≥ 10 orx ≥ 10
16 Write an inequality for this situation. The weight limit on an elevator is 3,500 pounds. Passengers and cargo weighing a total of 2,450 pounds are already on the elevator. Write an inequality that could be used to determine x, the possible additional weight the elevator can carry.2,450 + x < 3, or x + 2,450 < 3,500
17 Write about what you’ve learned: Complete Reading StrategiesUse complete sentences.Turn it over on your desk when done. It will be collected.Make sure your name, date, class period are on it!
18 Graphing Inequalities Words aren’t enough. I want to show an inequality on a number line. Can I do that?? Dr. Burger says yes! We can graph inequalities
19 Course 212-4InequalitiesYou 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.
20 Inequalities 12-4 a > 5 b ≤ 3 Course 212-4InequalitiesThis open circle shows that 5 is not a solution.a > 5If 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
21 Symbols Review Open Circle Closed Circle The number is not included in the solution.The number is included in the solution.
22 Additional Example 2: Graphing Simple Inequalities Course 212-4InequalitiesAdditional Example 2: Graphing Simple InequalitiesOn your own paper, graph each inequality.A. n < 33 is not a solution, sodraw an open circle at 3. Shade the line to the left of 3.–2 –B. a ≥ –4–4 is a solution, sodraw a closed circleat –4. Shade the lineto the right of –4.–6 –4 –
23 Inequalities 12-4 Check It Out: Example 2 Course 212-4InequalitiesCheck It Out: Example 2On your own paper, graph each inequality.A. p ≤ 22 is a solution, sodraw a closed circle at 2. Shade the line to the left of 2.–3 –2 –B. e > –2–2 is not a solution, sodraw an open circleat –2. Shade the lineto the right of –2.–3 –2 –
24 Insert Lesson Title Here Course 212-4InequalitiesInsert Lesson Title HereLesson Quiz: Part IIGraph the inequalities on your own paper.1. x > –1123–2. x < –1123–
25 Insert Lesson Title Here Course 212-4InequalitiesInsert Lesson Title HereLesson Quiz: Part IIGraph the inequalities, continued.3. x > –1123–4. x < –1123–
35 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?
36 Now go through each graph and fill in the inequalities Now go through each graph and fill in the inequalities. When you have finished, check with a partner close to you.
37 How did you do?! Temperature Check! Give me a thumbs up if you did a great job and didn’t miss anyGive me a sideways thumb if you did alright, but you probably need to work on it a little bitGive me a thumbs down if you aren’t getting it yet, and you need some help
38 Let’s get wordy!Who remembers some key words and phrases that tell us which inequality sign to choose? Raise your hand!
39 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…
40 Let’s finish up by writing word problems for the rest of the graphs Let’s finish up by writing word problems for the rest of the graphs. Try to do them on your own, and have you’re a partner check when you’ve finished.