0.8e: Exercises- Linear Inequalities
- Page ID
- 38278
A: Check a solution
Exercise \(\PageIndex{1}\)
\( \bigstar \) Determine whether or not the given value is a solution.
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- Answers to odd exercises:
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1. Yes 3. No 5. Yes 7. No 9. Yes
B: Solve Linear Inequalities
Exercise \(\PageIndex{2}\)
\( \bigstar \) Graph all solutions on a number line and provide the corresponding interval notation.
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- Answers to odd exercises:
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11. \(( - 3 , \infty )\);
Figure 1.8.11
13. \(( 1 , \infty )\);
15. \([ 0 , \infty )\);
17. \(( - \infty , 3 ]\);
19. \([ - 2 , \infty )\);
21. \(( - \infty , - 5 )\);
23. \([ - 8 , \infty )\);
25. \([ 5 , \infty )\);
27. \(( - \infty , 7 )\);
29. \(( - 1 , \infty )\);
31. \(( 3 , \infty )\);
33. \(\left( - \infty , - \dfrac { 3 } { 2 } \right]\);
35. \(\emptyset\);
37. \(( - \infty , 0 )\);
39. \(\mathbb { R }\);
41. \([ - 2 , \infty )\);
C: Solve Compound Linear Inequalities
Exercise \(\PageIndex{3}\)
\( \bigstar \) Graph all solutions on a number line and provide the corresponding interval notation.
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- Answers to odd exercises:
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43. \((- 1,4 )\);
45. \([0,4]\);
47. \((−5,5]\);
49. \((−4,3]\);
51. \([−4,1]\);
53. \((−∞,−1)∪(3,∞)\);
55. \((−∞,\frac{1}{2}]∪[\frac{5}{2},∞)\);
57. \(ℝ\);
59. \((−∞,5)\);
61. \((−∞,−10)\);
63. \([−3,2]\);
65. \((−∞,5)\);
67. \(Ø\);
69. \(−2\);
71. \((−\frac{1}{2},\frac{3}{2})\);
73. \([−1,3)\);
75. \((−8,−4)\);
77. \((−15,−5]\);
79. \((−5,20)\);
81. \([−\frac{1}{3}, \frac{4}{3}]\);
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