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INEQUALITIES AND THEIR GRAPHS TUESDAY SEPTEMBER 30

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I have been talking to the parents of many students in the past few weeks about students who are failing my class, and when they ask why their students are failing, I will mention that they do no homework, no class work, don’t participate, talk all class, sleep, use cell phones and such. And the parents always ask me, “Why am I just hearing this now?” COMMON EXPECTATIONS

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Behavior not conducive to good learning for all students equals referral COMMON EXPECTATIONS

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The good news: my experience with the students here at Rainier has made some changes in regard to how I treat the classes are in order. 1. Beverages are allowed. Don’t ruin this! 2. Cell phones are allowed during tests and free time. I will tell you when cell phones are appropriate. 3. Cell phones may be deemed okay during class work time in the future. COMMON EXPECTATIONS

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The Instructional Assistants in my classes are necessary and helpful. If you have any questions you can ask them. They are part of the team of teachers at this school. If I hear badmouthing or disrespectful comments about a teacher or an assistant, there will be a referral. COMMON EXPECTATIONS

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Class work time is meant to be a time for students to work collaboratively on the worksheet or project that day, not to distract other students who may need time to learn. This applies to students getting an A or getting an F. Don’t distract others. Any student not taking part in a classroom activity will be getting a referral. COMMON EXPECTATIONS

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Seating charts will be revised and their will be new assignments the Monday after Halloween. Seating assignments are based on a variety of criteria, and they aren’t random or punishment. If you have medical issues that require you to sit in the first row, make sure to let me know. Students that chose to ignore the seating assignments will be given a referral. COMMON EXPECTATIONS

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Cell Phone Policy: ZERO TOLERANCE Any time I think a student is using a cell phone, there will be a referral. COMMON EXPECTATIONS

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These actions are not taken as a punishment for the class, but because I want to make sure that students get the best education they can at this school. Even if you are an A student, the student next to you that is being distracted by your actions might not be. You should all be passing my class! If you need extra help or some tutoring please let me know so we can find a way to get you help! COMMON EXPECTATIONS

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You should all be familiar with inequalities. If a person wanted to ride the Shuttle Launch Experience at NASA, they would need to be 48 inches tall or taller. INEQUALITIES

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You should all be familiar with inequalities. We could express this as an inequality. Let the variable x represent any person x ≥ 48 inches INEQUALITIES

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This type of sign should be a familiar sight Let the variable x represent the speed of your vehicle x ≤ 55 miles per hour INEQUALITIES

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So we can write a variety of inequalities X is a number greater than 7 X > 7 Y is a number greater than or equal to 9 Y ≥ 9 Z is a number less than 12 Z < 12 A is a number less than or equal to 1000 A ≤ 1000 INEQUALITIES

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Inequalities can also be more complicated: All real numbers 7 less than Q that are greater than -12 Q – 7 > -12 All real numbers 12 more than the product of R and 7 that are less than 0 7R + 12 < 0 INEQUALITIES

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Just like with equations, we can determine whether given numbers are solutions of an inequality, or whether or not they make the statement true. Simply take the number and substitute it into the inequality and see if the statement is true or not INEQUALITIES

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Our first example was X > 7 Is X = 3 a solution to the inequality? 3 > 7 So X = 3 is not a solution to the inequality Is X = 9 a solution to the inequality? 9 > 7 So X = 9 is a solution to the inequality INEQUALITIES

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Our second example was Y ≥ 9 Is Y = 3 a solution to the inequality? Is Y = 9 a solution to the inequality? Our third example was Z < 12 Is Z = 3 a solution to the inequality? Is Z = 12 a solution to the inequality INEQUALITIES

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Let’s try our complicated examples: Q – 7 > -12 Is Q = 2 a solution to the inequality? 2 – 7 > > -12 Sometimes these can be complicated to solve… INEQUALITIES

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Sometimes it helps to use a number line to determine whether a number is a solution to an inequality. Say for example x < 4. Let’s graph this inequality: INEQUALITIES

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To start with, because x can’t equal 4, we need to draw an open circle around 4: x < 4 INEQUALITIES

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Next, because all numbers less than 4 are solutions to the inequality, we can draw a solid line: x < 4 So all of the numbers less than 4, but not equal to 4, are solutions to this inequality. INEQUALITIES

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Let’s try another example: x ≥ -3 First, because x can equal -3, we can draw a solid circle around -3: INEQUALITIES

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x ≥ -3 And because all of the numbers greater than -3 are solutions to the inequality, we can draw a line to the right of -3 INEQUALITIES

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Let’s go back to our complicated examples: Q – 7 > -12 Is Q = 2 a solution to the inequality? 2 – 7 > > -12 Let’s graph those numbers to make sure whether -5 is greater than -12 INEQUALITIES

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Do Now: Problems 8-38 even, page 168 HOMEWORK

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