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Bell Work

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Vocabulary Inequality – a mathematical statement that shows the relationship between quantities that are not equivalent. Algebraic Inequality – an inequality that contains at least one variable. Solution Set – the set of values that make a statement true. Compound Inequality – a combination of more than one inequality. These need to be added to your cards (27).

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≥ ≤ > < Word PhrasesMeaningSymbol 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 Symbols you will see with Inequalities:

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Write an inequality for each situation. A. There are at least 15 people in the waiting room. number of people ≥ 15 B. The tram attendant will allow no more than 60 people on the tram. number of people ≤ 60 “At least” means greater than or equal to. “No more than” means less than or equal to. Writing Inequalities

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Write an inequality for each situation. A. There are at most 10 gallons of gas in the tank. gallons of gas ≤ 10 B. There is at least 10 yards of fabric left. yards of fabric ≥ 10 “At most” means less than or equal to. “At least” means greater than or equal to. Writing Inequalities

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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. 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. Graphing Inequalities

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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

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Graph each inequality. –3 –2 –1 0 1 2 3 A. n < 3 3 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 circle at –4. Shade the line to the right of –4. Let’s Graph These:

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Graph each inequality. –3 –2 –1 0 1 2 3 A. p ≤ 2 2 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 circle at –2. Shade the line to the right of –2. Now You Try!

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A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related. x > 3 or x < –1–2 < y and y < 4 x is either greater than 3 or less than–1. y is both greater than –2 and less than 4. y is between –2 and 4. The compound inequality –2 < y and y < 4 can be written as –2 < y < 4. Writing Math Compound Inequalities

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Graph each compound inequality. 0 1 2 3 456 1 2 3 456 – – ––– – m ≤ –2 or m > 1 First graph each inequality separately. m ≤ –2m > 1 Then combine the graphs. 0 246 246 –– – 0 2 4 6 –2–4 –6 º The solutions of m ≤ –2 or m > 1 are the combined solutions of m ≤ –2 or m > 1. Graphing Compound Inequalities

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Graph each compound inequality –3 < b ≤ 0 –3 < b ≤ 0 can be written as the inequalities –3 < b and b ≤ 0. Graph each inequality separately. –3 < b b ≤ 0 0 2 4 6 24 6 ––– 0 2 4 6 –2–4 –6 º Then combine the graphs. Remember that –3 < b ≤ 0 means that b is between –3 and 0, and includes 0. 0 1 2 3 456 1 2 3 456 – – ––– – Graphing Compound Inequalities

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–3 –3. Reading Math Hint, Hint!!!

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Exit Ticket: Write an inequality for each situation. 1. No more than 220 people are in the theater. 2. There are at least a dozen eggs left. 3. Fewer than 14 people attended the meeting. number of eggs ≥ 12 people in the theater ≤ 220 people attending the meeting < 14

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