Interval Notation: - UH



Interval Notation:

[pic]

[pic]

Example:

[pic]

Solution:

[pic]

[pic]

[pic]

[pic]

Example:

[pic]

Solution:

[pic]

[pic]

Example:

[pic]

Solution:

[pic]

[pic]

[pic]

[pic]

Additional Example 1:

[pic]

Solution:

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Additional Example 2:

[pic]

Solution:

[pic]

[pic]

[pic]

Additional Example 3:

[pic]

Solution:

[pic]

[pic]

[pic]

[pic]

Additional Example 4:

[pic]

Solution:

[pic]

[pic]

Additional Example 5:

[pic]

Solution:

[pic]

[pic]

Additional Example 6:

[pic]

Solution:

[pic]

[pic]

[pic]

[pic]

[pic]

Additional Example 7:

[pic]

Solution:

[pic]

[pic]

[pic]

[pic]

[pic]

For each of the following inequalities:

(a) Write the inequality algebraically.

(b) Graph the inequality on the real number line.

(c) Write the inequality in interval notation.

1. x is greater than 5.

2. x is less than 4.

3. x is less than or equal to 3.

4. x is greater than or equal to 7.

5. x is not equal to 2.

6. x is not equal to [pic].

7. x is less than [pic]

8. x is greater than [pic].

9. x is greater than or equal to [pic].

10. x is less than or equal to [pic].

11. x is not equal to [pic].

12. x is not equal to 3.

13. x is not equal to 2 and x is not equal to 7.

14. x is not equal to [pic] and x is not equal to 0.

Write each of the following inequalities in interval notation.

15. [pic]

16. [pic]

17. [pic]

18. [pic]

19. [pic]

20. [pic]

21. [pic]

22. [pic]

Write each of the following inequalities in interval notation.

23.

24.

25.

26.

27.

28.

Given the set [pic], use substitution to determine which of the elements of S satisfy each of the following inequalities.

29. [pic]

30. [pic]

31. [pic]

32. [pic]

33. [pic]

34. [pic]

For each of the following inequalities:

a) Solve the inequality.

b) Graph the solution on the real number line.

c) Write the solution in interval notation.

35. [pic]

36. [pic]

37. [pic]

38. [pic]

39. [pic]

40. [pic]

41. [pic]

42. [pic]

43. [pic]

44. [pic]

45. [pic]

46. [pic]

47. [pic]

48. [pic]

49. [pic]

50. [pic]

51. [pic]

52. [pic]

53. [pic]

54. [pic]

55. [pic]

56. [pic]

57. [pic]

58. [pic]

Which of the following inequalities can never be true?

59. (a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

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