1 / 85

Nov. 9 - Inequalities in Two Variables

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

cocoore
Download Presentation

Nov. 9 - Inequalities in Two Variables

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related