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HW # 77 - p . 146 & 147 # 1-44 even Warm up

Week 23, Day Two. HW # 77 - p . 146 & 147 # 1-44 even Warm up. Solve . 1. 2 x + 8 = x – 7 2. –4( x + 3) = –5 x – 2 3. 5 x + x + (–11) = 25 – 3 x 4. 6 n + 9 – 4 n = 3 n. x = –15. x = 10. x = 4. n = 9. Warm Up Response. ~$. Homework Check.

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HW # 77 - p . 146 & 147 # 1-44 even Warm up

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  1. Week 23, Day Two HW # 77 - p. 146 & 147 # 1-44 even Warm up Solve. 1. 2x + 8 = x – 7 2. –4(x + 3) = –5x – 2 3. 5x + x + (–11) = 25 – 3x 4. 6n + 9 – 4n = 3n x = –15 x = 10 x = 4 n = 9

  2. Warm Up Response ~$

  3. Homework Check p. 142 & 143 # 1-40 even

  4. Goals for Today • 3-7 Solving Inequalities by Multiplying or Dividing • Examples and Notes • CW: Inequalities 1 & 2 worksheets

  5. Extra slides for practice

  6. When you multiply (or divide) both sides of an inequality by a negative number, you must reverse the inequality symbol to make the statement true.

  7. Remember! When graphing an inequality on a number line, an open circle means that the point is not part of the solution and a closed circle means that the point is part of the solution.

  8. a 4 4• 12 < 4 • Additional Example 1A: Solving Inequalities by Multiplying or Dividing Solve and graph. a 4 12 < Multiply both sides by 4. 48 < a, or a > 48 43 44 45 46 47 48 49 50 51 52 53 54

  9. 12 < 12.25 12 < 12 < 12 < 11.75 12 < 12 < a 4 a 4 49 4 47 4 ? ? ? ? Additional Example 1A Continued Check According to the graph, 49 should be a solution and 47 should not be a solution. Substitute 49 for a. Substitute 47 for a. x So 49 is a solution. So 47 is not a solution.

  10. 45–9 –9b–9 ≥ Additional Example 1B: Solving Inequalities by Multiplying or Dividing Solve and graph. –9b ≤ 45 Divide both sides by –9; ≤ changes to ≥. b ≥ –5 0 –5

  11. b 5 5• 16 > 5 • Check It Out! Example 1A Solve and graph. b 5 16 > Multiply both sides by 5. 80 > b, or b < 80 73 74 75 76 77 78 79 80 81 82 83 84

  12. 16 > 15.8 16 > 16 > 16 > 16.2 16 > 16 > b 5 b 5 79 5 81 5 ? ? ? ? Check It Out! Example 1A Continued Check According to the graph, 79 should be a solution and 81 should not be a solution. Substitute 79 for b. Substitute 81 for b. x So 79 is a solution. So 81 is not a solution.

  13. –4a–4 12–4 ≥ Check It Out! Example 1B Solve and graph. 12 ≤ –4a Divide both sides by –4; ≤ changes to ≥. –3 ≥ a 0 –3

  14. Additional Example 2: Problem Solving Application A rock-collecting club needs to make at least $500. They are buying rocks for $2.50 and selling them for $4.00. What is the least number of rocks the club must sell to make the goal?

  15. 1 Understand the Problem rocks bought $ rocks sold $ ≥ # of rocks $500 - • Additional Example 2 Continued The answer is the least number of rocks the club must sell to make their goal. List the important information: • The club needs to make at least $500. • The club is buying rocks for $2.50. • The club is selling rocks for $4.00. Show the relationship of the information:

  16. Make a Plan r - • ≥ 2.50 $500 4.00 2 Additional Example 2 Continued Use the information to write an inequality. Let r represent the number of rocks.

  17. 3 Solve 1.50r ≥ 500 1.501.50 Additional Example 2 Continued (4.00 – 2.50) • r ≥ 500 Simplify. 1.50r ≥ 500 Divide both sides by 1.50. r ≥ 333.33… 334 rocks need to be sold in order for the club to make at least $500.

  18. 4 Additional Example 2 Continued Look Back Since the rock-collecting club is reselling rocks, they are making a $1.50 profit from each rock. $1.50(334) ≥ $500, or $501 ≥ $500.

  19. Check It Out! Example 2 The music club needs to make at least 3 times more than the language club made ($132) in order to go to the symphony. They are selling music sheet holders for $3.75. What is the number of music sheet holders the club must sell to make the goal?

  20. 1 Understand the Problem Check It Out! Example 2 Continued The answer is the least number of music sheet holders the club must sell to make their goal. List the important information: • The club needs to make at least three times the amount of the language club ($132). • The club is selling music sheet holders for $3.75. Show the relationship of the information: selling price of music holders # of sheet holders • ≥ 3 • $132

  21. Make a Plan 2 Check It Out! Example 2 Continued Use the information to write an inequality. Let m represent the number of music sheet holders. m $3.75 • ≥ 3 • $132

  22. 3 Solve 3.75m ≥ 396 3.753.75 Check It Out! Example 2 Continued 3.75 • m ≥ 3 • 132 Simplify. 3.75m ≥ 396 Divide both sides by 3.75. m ≥ 106 106 music sheet holders must be sold in order for the music club to make at least three times the amount of the language club or $396.

  23. For the music club to make as much money as the language club they would need to sell or 35.2, or 36, music sheet holders. In order to make three times the amount it would take 3(36) or 108 • $3.75 = $405 ≥ $396. 132 3.75 4 Check It Out! Example 2 Continued Look Back

  24. –2 0 2 40 50 45 x q 3 8 -8 -6 -4 -2 45 40 Lesson Quiz: Part I Solve and graph. 1. –14x > 28 x< –2 2. < 15 x< 45 3. 18< –6x –3 > x 4. 5 q ≥ 40

  25. Lesson Quiz: Part II 5. Jared isn’t supposed to carry more than 35 pounds in his backpack. He has 8 textbooks and each book weighs 5 pounds. What is the greatest amount of textbooks he can carry in his backpack at one time? No more than 7

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