SECTION 1.7 Interval Notation and Linear Inequalities
Interval Notation:
Example:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
Example:
Solution:
Example:
SECTION 1.7 Interval Notation and Linear Inequalities
Solution:
Additional Example 1:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
Additional Example 2:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
Additional Example 3:
Solution:
Additional Example 4:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
Additional Example 5:
Solution:
Additional Example 6:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
Additional Example 7:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
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 5 .
7.
x is less than 1.
8.
x is greater than 6 .
9.
x is greater than or equal to 4 .
10. x is less than or equal to 2 .
11. x is not equal to 8 .
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 4 and x is not equal to 0.
Write each of the following inequalities in interval notation.
15. x  3
16. x  5
17. x  2
18. x  7
19. 3  x  5
20. 7  x  2
21. x  7
22. x  9
SECTION 1.7 Interval Notation and Linear Inequalities
Write each of the following inequalities in interval notation.
23.
24.
25.
26.
27.
28.
  



















   




   




   






Given the set S  2, 4,  3, 13 , use substitution to determine which of the elements of S satisfy each
of the following inequalities.
29. 2 x  5  10
30. 4 x  2  14
31. 2 x  1  7
32. 3x  1  0
33. x 2  1  10
34.
1 2

x 5
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. 2 x  10
36. 3x  24
37. 5x  30
SECTION 1.7 Interval Notation and Linear Inequalities
38. 4 x  40
39. 2 x  5  11
40. 3x  4  17
41. 8  3x  20
42. 10  x  0
43. 4 x  11  7 x  4
44. 5  9 x  3x  7
45. 10 x  7  2 x  6
46. 8  4 x  6  5x
47. 5  8x  4 x  1
48. x  10  8x  9
49. 3(4  5x)  2(7  x)
50. 4(3  2 x)  ( x  20 )
51.
5
6
 13 x  12 ( x  5)
52.
2
5
x  12    13 10  x
53. 10  3x  2  8
54. 9  2 x  3  13
55. 4  3  7 x  17
56. 19  5  4 x  3
57.
2
3
 3 x1510 
58.
3
4
 562 x   53
4
5
Which of the following inequalities can never be true?
59. (a)
5 x9
(b)
9 x5
(c)
3  x  7
(d)
5  x  3