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Do Now 12/11/09

Do Now 12/11/09. Copy HW in your planner. Text p. 359, #4-14 even 22-36 even. In your journal, 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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Do Now 12/11/09

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  1. Do Now 12/11/09 • Copy HW in your planner. • Text p. 359, #4-14 even 22-36 even. • In your journal, 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?

  2. Chapter 6 Preview “Solving and Graphing Linear Inequalities” (6.1) Solve Inequalities Using Addition and Subtraction (6.2) Solve Inequalities Using Multiplication and Division (6.3) Solve Multi-Step Inequalities (6.4) Solve Compound Inequalities (6.5) Solve Absolute Value Equations (6.6) Solve Absolute Value Inequalities (6.7) Graph Linear Inequalities in Two Variables Winter break

  3. Section 6.1“Solve Inequalities Using Addition and Subtraction” INEQUALITIES – mathematical sentence formed by placing a <, ≤, >, or ≥ between two expressions. 13 * 22 ≥14 - z 5 ÷ x > 30 y² – 8 < 12 11 - a ≤121

  4. Writing Equations with Inequalities

  5. On a number line, the GRAPH OF AN INEQUALITY is the set of points that represent ALL SOLUTIONS of the inequality. “Less than” and “greater than” are represented with an open circle. Graph x < 8 5 6 7 8 9 10 11 “Less than or equal to” and “greater than or equal to” are represented with a closed circle. Graph x ≥ 11 8 9 10 11 12 13 14 15

  6. 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. SOLUTION Let Trepresent a temperature (in degrees Fahrenheit) in the United States. The value of Tmust be less than or equal to 134. So, an inequality is T≤ 134.

  7. 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. Write an inequality represented by the graph. SOLUTION

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

  9. Solving an Inequality… Isolate the variable! Get ‘m’ by itself. m + 4 < 12 To get the ‘m’ by itself get rid of “adding 4.” • 4 • 4 Do the opposite. “Subtract 4.” m < 8 Whatever you do to one side of the Inequality you must do the other side.

  10. Solving an Inequality… Isolate the variable! Get ‘n’ by itself. n - 5 ≥ 6 To get the ‘n’ by itself get rid of “subtracting 5.” +5 + 5 Do the opposite. “Add 5.” n ≥ 11 Whatever you do to one side of the inequality you must do the other side.

  11. Solve x – 5 > – 3.5.Graph your solution. ANSWER The solutions are all real numbers greater than 1.5. Check by substituting a number greater than 1.5 for xin the original inequality. x – 5 > – 3.5 Write original inequality. x – 5+5> – 3.5+5 Add 5 to each side. x > 1.5 Simplify.

  12. Solve p – 9.2 < – 5.Graph your solution. ANSWER The solutions are all real numbers less than 4.2. Check by substituting a number less than 4.2 for xin the original inequality. SOLUTION p – 9.2 < – 5 Write original inequality. p – 9.2+9.2 < – 5+9.2 Add 9.2 to each side. x < 4.2 Simplify.

  13. Solve 9x+ 7. Graph your solution. ANSWER You can rewrite2 ≥ x asx ≥ 2. The solutions are all real numbers less than or equal to 2. > 9≥ x+ 7 Write original inequality. 9– 7 ≥x+ 7 – 7 Subtract 7 from each side. 2 ≥ x Simplify.

  14. ANSWER You can rewrite 0.5 < yas y > 0.5 . The solutions are all real numbers greater than or equal to 0.5 . Solve y+ 5.5 > 6. Graph your solution. SOLUTION y+ 5.5 > 6 Write original inequality. y+ 5.5 –5.5> 6 –5.5 Subtract 5.5 from each side. y> 0.5 Simplify.

  15. You are checking a bag at an airport. Bags can weigh no more than 50 pounds. Your bag weighs 16.8 pounds. Find the possible weightsw(in pounds) that you can add to the bag. Solve a real-world problem LUGGAGE WEIGHTS SOLUTION Write a verbal model. Then write and solve an inequality. 16.8 + w ≤ 50

  16. 16.8+ w 50 16.8 + w –16.8 50 –16.8 ANSWER You can add no more than33.2pounds. < < Solve a real-world problem Write inequality. Subtract 16.8 from each side. Simplify. w ≤ 33.2

  17. Write and solve an inequality to find the possible values of x. • Perimeter ≤ 51.3 feet 14.2 + 15.5 + x ≤ 51.3 14.2 ft 29.7 + x ≤ 51.3 x ft x ≤ 21.6 15.5 ft

  18. Algebra in “Real-Life!” • In your groups, complete the “real-life” activity. • Interdisciplinary Application “Bald Eagles”

  19. Algebra in “Real-Life!” • In your groups, complete the two “real-life” activities. • Interdisciplinary Application “Bald Eagles” • 1) y = 393x + 14,324 • 2) graph • 3) approximately 18,254 • 4) habitat loss, less people counting • 5) y = 512.5x + 13,698 • 6) graph • 7) approximately 18,880

  20. Homework NJASK7 Prep • Text p. 359, #4-14 even 22-36 even 24

  21. 2) x > -2 4) x ≥ -7 6) x ≤ -1 8) n ≤ 12 10) m < 1 12) x ≤ -7.5 14) y < 4.8 16) d > 10.2 18) m – 3 ≥ 10; m ≥ 13 20) 85 > x – 63; x > 148 22) 17 hats or less 24) a). 6532 + 4887 < 5034 + s; s > 6385 b). Yes, because 6392 > 6385. No, because 6385 is not > 6385. No, because 6377 is not > 6385. Practice Worksheet Form B#2-24 even

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