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Do Now 3/5/14 Take out HW from last night. Take out HW from last night. –Text p. 463, #2-36 evens Copy HW in your planner. Copy HW in your planner. –Practice worksheet 11.4 B In your notebook, answer the following question. Outside of the math classroom, where have you heard phrases such as “at least” or “no more than”? Give examples. How would you write the phrases mathematically? In your notebook, answer the following question. Outside of the math classroom, where have you heard phrases such as “at least” or “no more than”? Give examples. How would you write the phrases mathematically?

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Homework Text p. 463, #2-36 evens Homework Text p. 463, #2-36 evens 2) isolate the variable 2) isolate the variable 4) proportion 4) proportion 6) -81 6) -81 8) 12 8) 12 10) 7/6 or 1 1/6 10) 7/6 or 1 1/6 12) 7/99 12) 7/99 14) -9 14) -9 16) 8 16) 8 18) 25 18) 25 20) -47 20) -47 22) 5 22) 5 24) -0.75 24) -0.75 26) 26 26) 26 28) 1/8 28) 1/8 30) 4.5 30) 4.5 32) 87.5 32) 87.5 34) 5 34) 5 36) 45 36) 45

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Objective SWBAT read and write inequalities and graph them on a number line SWBAT read and write inequalities and graph them on a number line

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Section 11.4, “Inequalities” Section 11.4, “Inequalities” INEQUALITIES – INEQUALITIES – mathematical sentence formed by placing a, or ≥ between two expressions. mathematical sentence formed by placing a, or ≥ between two expressions. y – 8 < 12 y – 8 < 12 13 ≥ 14 - z 13 ≥ 14 - z 11 + a ≤ 121 11 + a ≤ 121 x +8 > 30 x +8 > 30

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Writing Inequalities SymbolMeaning Key Phrase Is less than Fewer than, below Is less or equal to At most, no more than Is greater than More than, above Is greater than or equal to At least, no less than < ≤ >

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On a number line, the GRAPH OF AN INEQUALITY is the set of points that represent the SOLUTION SET of the inequality. On a number line, the GRAPH OF AN INEQUALITY is the set of points that represent the SOLUTION SET of the inequality. x < 8 x < 8 5678 x ≥ 11 x ≥ 11 1213111410 “Less than” and “greater than” are represented with an open circle. “Less than or equal to” and “greater than or equal to” are represented with a closed circle. 10911 89

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Graph each inequality x < -3 x < -3 -6-5-4-3 x ≥ 7 x ≥ 7 897106 “Less than” and “greater than” are represented with an open circle. “Less than or equal to” and “greater than or equal to” are represented with a closed circle. -20 45

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Graph each inequality 7 ≥ y 7 ≥ y 897106 “Less than or equal to” and “greater than or equal to” are represented with a closed circle. 45 -1 < h -1 < h -4-3-2 “Less than” and “greater than” are represented with an open circle. 102

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SOLUTION Write an inequality represented by the graph. The closed circle means that 8 is not a solution of the inequality. Because the arrow points to the left, all numbers less than 8 are solutions. ANSWER An inequality represented by the graph is x < 8.

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SOLUTION The closed circle means that – 2.5 is a solution of the inequality. Because the arrow points to the right, all numbers greater than – 2.5 are solutions. ANSWER An inequality represented by the graph is x > – 2.5. Write an inequality represented by the graph.

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SOLUTION The highest temperature recorded in the United States was 134°F at Death Valley, California, in 1913. Use only this fact to write and graph an inequality that describes the temperatures in the United States. Let T represent a temperature (in degrees Fahrenheit) in the United States. The value of T must be less than or equal to 134. So, an inequality is T ≤ 134.

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COMPOUND INEQUALITY – COMPOUND INEQUALITY – consists of two separate inequalities joined by AND or OR.

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“AND” Compound Inequalities The graph of a compound inequality with AND is the INTERSECTION of the graphs of the inequalities. The graph of a compound inequality with AND is the INTERSECTION of the graphs of the inequalities. Graph x > -2 012 -2 3 Graph x ≤ 1 012-23 Graph of x ≤ 1 and x > -2 012-23 Graph -2< x ≤ 1 Graph -2< x ≤ 1

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“OR” Compound Inequalities The graph of a compound inequality with OR is the UNION of the graphs of the inequalities. The graph of a compound inequality with OR is the UNION of the graphs of the inequalities. Graph x > 2 012 -2 3 Graph x ≤ -1 012-23 Graph of x ≤ -1 or x > 2 012-23

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Graph each compound inequality 5 < y ≤ 9 5 < y ≤ 9 897106 4 5 h > 1 or h ≤ -3 h > 1 or h ≤ -3 -4-3-2 102

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Graph each compound inequality y ≤ 16 or y > 20 y ≤ 16 or y > 20 1819172016 14 15 h > -3 and h ≤ 0 h > -3 and h ≤ 0 -4-3-2 102

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Translate the verbal phrase into an inequality. Then graph the inequality. All real numbers that are greater than – 2 and less than 3. Inequality : Graph: All real numbers that are less than 0 or greater than or equal to 2. Inequality:Graph: – 2 < x < 3 x < 0 or x ≥ 2 Challenge

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Homework Practice worksheets 11.4 B & C

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