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1.4 “solving linear inequalities”

1.4 “solving linear inequalities”. ex 1:. Graph x > 3. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10. ex 1:. Graph x > 3.

raymond-sheppard
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1.4 “solving linear inequalities”

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  1. 1.4 “solving linear inequalities”

  2. ex 1: Graph x > 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  3. ex 1: Graph x > 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  4. ex 1: Graph x > 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real numbers greater than three”

  5. ex 2: Graph x  –2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  6. ex 2: Graph x  –2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  7. ex 2: Graph x  –2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real numbers less than or equal to negative two”

  8. ex 3: Solve 5x – 8 < 12

  9. ex 3: Solve 5x – 8 < 12 +8 +8

  10. ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20

  11. ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5

  12. ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5 x < 4

  13. ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x < 4

  14. ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x < 4

  15. ex 4: Solve –3x  12

  16. ex 4: Solve –3x  12 –3 –3

  17. ex 4: Solve –3x  12 –3 –3 x –4

  18. ex 4: Solve –3x  12 –3 –3 x –4 rule: When you multiply or divide by a negative , the inequality sign switches direction.

  19. ex 5: Solve 2x + 1  6x – 23

  20. ex 5: Solve 2x + 1  6x – 23 –2x –2x

  21. ex 5: Solve 2x + 1  6x – 23 –2x –2x 1  4x – 23

  22. ex 5: Solve 2x + 1  6x – 23 –2x –2x 1  4x – 23 +23 +23

  23. ex 5: Solve 2x + 1  6x – 23 –2x –2x 1  4x – 23 +23 +23 24  4x

  24. ex 5: Solve 2x + 1  6x – 23 –2x –2x 1  4x – 23 +23 +23 24  4x 4 4

  25. ex 5: Solve 2x + 1  6x – 23 –2x –2x 1  4x – 23 +23 +23 24  4x 4 4 6  x

  26. ex 5: Solve 2x + 1  6x – 23 –2x –2x 1  4x – 23 +23 +23 24  4x 4 4 6  x VARIABLES ON THE LEFT-SIDE !

  27. ex 5: Solve 2x + 1  6x – 23 –2x –2x 1  4x – 23 +23 +23 24  4x 4 4 6  x VARIABLES ON THE LEFT-SIDE ! x 6

  28. ex 6: Graph x > –5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  29. ex 6: Graph x > –5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  30. ex 6: Graph x > –5 Graph x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  31. ex 6: Graph x > –5 Graph x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  32. ex 6: Graph x > –5 Graph x < 7 Graph x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  33. ex 6: Graph x > –5 Graph x < 7 Graph x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  34. compound inequality

  35. compound inequality Two simple inequalities joined by “and” or “or”

  36. compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  37. compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  38. compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real #s that are greater than negative five and less than seven”

  39. compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real #s that are greater than negative five and less than seven” –5 < x < 7

  40. compound inequality Two simple inequalities joined by “and” or “or”

  41. compound inequality Two simple inequalities joined by “and” or “or” x < –5 or x >7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  42. compound inequality Two simple inequalities joined by “and” or “or” x < –5 or x >7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  43. compound inequality Two simple inequalities joined by “and” or “or” x < –5 or x >7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real #s that are less than negative five or greater than seven”

  44. ex 7: Solve –2  3x – 8  4

  45. ex 7: Solve –2  3x – 8  4 +8 +8 +8

  46. ex 7: Solve –2  3x – 8  4 +8 +8 +8 6  3x  12

  47. ex 7: Solve –2  3x – 8  4 +8 +8 +8 6  3x  12 3 3 3

  48. ex 7: Solve –2  3x – 8  4 +8 +8 +8 6  3x  12 3 3 3 2  x  4

  49. ex 7: Solve –2  3x – 8  4 +8 +8 +8 6  3x  12 3 3 3 2  x  4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x  2 and x  4

  50. ex 7: Solve –2  3x – 8  4 +8 +8 +8 6  3x  12 3 3 3 x  2 and x  4 2  x  4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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