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Nov. 9 - Inequalities in Two Variables

Algebra 1<br>middle school math<br>high school math

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Nov. 9 - Inequalities in Two Variables

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  1. scrapple day! 11.09.22 Take out your spiral for a warm-up. Would you rather have the only beverage you can drink be water or the only food you can eat be salad? Agenda: • Warm-up • Notes: Inequalities • Desmos Activity Pencil, Calculator, Spiral

  2. Warm-up Name_____________ Directions: Complete in your spiral. • Copy. Solve. Graph. 16 - (4n - 2) > 2(3n + 14) 2. The perimeter of a rectangle is at most 24m. Two opposite sides are both 4m long. What are the possible lengths of the other two sides?

  3. Warm-up - Answers Name_____________ Directions: Complete in your spiral. • Copy. Solve. Graph. 16 - (4n - 2) > 2(3n + 14) 16 - 4n +2 > 6n + 28 -4n +18 > 6n +28 -6n -6n -10n + 18 > 28 -18 -18 -10n > 10 -10 -10 n < -1 2. The perimeter of a rectangle is at most 24m. Two opposite sides are both 4m long. What are the possible lengths of the other two sides?

  4. Warm-up - Answers Name_____________ Directions: Complete in your spiral. • Copy. Solve. Graph. 16 - (4n - 2) > 2(3n + 14) 16 - 4n +2 > 6n + 28 -4n +18 > 6n +28 -6n -6n -10n + 18 > 28 -18 -18 -10n > 10 -10 -10 n < -1 2. The perimeter of a rectangle is at most 24m. Two opposite sides are both 4m long. What are the possible lengths of the other two sides?2x +2(4) < 24 2x + 8 < 24 -8 -8 2x < 16 2 2 x < 8

  5. Inequalities In Two Variables >>>>>>>>>>>>> >>>>>>>>>>>>>

  6. Remember, in one variable inequalities: > < open circle >< closed circle Multiplying or dividing by a negative number requires the inequality to change direction. Inequalities In Two Variables

  7. To graph in two variables: • plot points for the line as usual • determine solid or dashed line • shade using a test point > < dashed line >< solid line Inequalities In Two Variables

  8. Ex. 1: Inequalities In Two Variables

  9. y > ½ x - 4 Inequalities In Two Variables

  10. y > ½ x - 4 Inequalities In Two Variables

  11. y > ½ x - 4 Inequalities In Two Variables

  12. y > ½ x - 4 Inequalities In Two Variables

  13. y > ½ x - 4 Inequalities In Two Variables

  14. y > ½ x - 4 Inequalities In Two Variables

  15. y > ½ x - 4 Inequalities In Two Variables

  16. y > ½ x - 4 The line is dashed because the sign is “greater than”. Inequalities In Two Variables

  17. y > ½ x - 4 The line is dashed because the sign is “greater than”. Inequalities In Two Variables

  18. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. Inequalities In Two Variables

  19. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. We use (0,0) to make the computation easiest. The only time we cannot use (0,0) is when it is on the line. Inequalities In Two Variables

  20. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. Inequalities In Two Variables

  21. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. Inequalities In Two Variables

  22. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. Inequalities In Two Variables

  23. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. Inequalities In Two Variables

  24. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. Inequalities In Two Variables

  25. y > ½ x - 4 Test (0,0): y > ½ x - 4 0 > ½ (0) - 4 ? 0 > 0 - 4 ? 0 > -4 ? Yes, (0,0) is on the solution side. Inequalities In Two Variables

  26. y > ½ x - 4 The solution region is a half-plane. All points in the shaded region make the inequality true. In this case, points on the line are NOT solutions to the inequality. Inequalities In Two Variables

  27. Ex. 2: Inequalities In Two Variables

  28. y > -3x + 5 Inequalities In Two Variables

  29. y > -3x + 5 Inequalities In Two Variables

  30. y > -3x + 5 Inequalities In Two Variables

  31. y > -3x + 5 Inequalities In Two Variables

  32. y > -3x + 5 Inequalities In Two Variables

  33. y > -3x + 5 The line is solid because the sign is “greater than or EQUAL TO”. Inequalities In Two Variables

  34. y > -3x + 5 The line is solid because the sign is “greater than or EQUAL TO”. Inequalities In Two Variables

  35. y > -3x + 5 Test (0,0): Inequalities In Two Variables

  36. y > -3x + 5 Test (0,0): y > -3x + 5 Inequalities In Two Variables

  37. y > -3x + 5 Test (0,0): y > -3x + 5 0 > -3(0) + 5 ? Inequalities In Two Variables

  38. y > -3x + 5 Test (0,0): y > -3x + 5 0 > -3(0) + 5 ? 0 > 0 + 5 ? Inequalities In Two Variables

  39. y > -3x + 5 Test (0,0): y > -3x + 5 0 > -3(0) + 5 ? 0 > 0 + 5 ? 0 > 5 ? Inequalities In Two Variables

  40. y > -3x + 5 Test (0,0): y > -3x + 5 0 > -3(0) + 5 ? 0 > 0 + 5 ? 0 > 5 ? No, (0,0) is NOT on the solution side. Inequalities In Two Variables

  41. y > -3x + 5 Test (0,0): y > -3x + 5 0 > -3(0) + 5 ? 0 > 0 + 5 ? 0 > 5 ? No, (0,0) is NOT on the solution side. Inequalities In Two Variables

  42. y > -3x + 5 The solution region is a half-plane. All points in the shaded region make the inequality true. In this case, points on the line ARE solutions to the inequality. Inequalities In Two Variables

  43. Ex. 3: Inequalities In Two Variables

  44. 4x - 2y < 16 Inequalities In Two Variables

  45. 4x - 2y < 16 First convert the equation to slope-intercept form. Inequalities In Two Variables

  46. 4x - 2y < 16 -4x -4x -2y < -4x + 16 -2 -2 y > 2x - 8 Inequalities In Two Variables

  47. 4x - 2y < 16 -4x -4x -2y < -4x + 16 -2 -2 y > 2x - 8 Inequalities In Two Variables

  48. 4x - 2y < 16 -4x -4x -2y < -4x + 16 -2 -2 y > 2x - 8 Inequalities In Two Variables

  49. 4x - 2y < 16 -4x -4x -2y < -4x + 16 -2 -2 y > 2x - 8 Inequalities In Two Variables

  50. 4x - 2y < 16 -4x -4x -2y < -4x + 16 -2 -2 y > 2x - 8 **Notice the inequality sign changed direction. Inequalities In Two Variables

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