Exercises 17.1, page 474

1. $x + 1 < 0$ $x + 1 < 0$ is true for all values of x less than $- 1; x < - 1 .$ $- 1; x < - 1 .$
3. $- 2 > - 4,$ $- 2 > - 4,$ multiplied by $- 3$ $- 3$ gives $6 < 12;$ $6 < 12;$ divided by $- 2$ $- 2$ gives $1 < 2 .$ $1 < 2 .$
5. $9 < 14$ $9 < 14$
7. $16 < 36$ $16 < 36$
9. $- 4 > - 9$ $- 4 > - 9$
11. $16 < 81$ $16 < 81$
13. $x > - 2$ $x > - 2$
15. $x \leq 38$ $x \leq 38$
17. $1 < x < 7$ $1 < x < 7$
19. $x < - 5$ $x < - 5$ or $x \geq 3$ $x \geq 3$
21. $x < 1$ $x < 1$ or $3 < x \leq 5$ $3 < x \leq 5$
23. $- 2 < x < 2$ $- 2 < x < 2$ or $3 \leq x < 4$ $3 \leq x < 4$
25. x is greater than 0 and less than or equal to 9.
27. x is less than $- 10,$ $- 10,$ or greater than or equal to 10 and less than 20.
29.
31.
33.
35.
37.
39.
41.
43.
45. Absolute inequality
47. No, $a - b < 0$ $a - b < 0$
49. $| x | + | y | > | x + y |$ $| x | + | y | > | x + y |$
51. From step (4) to step (5), both sides divided by log 0.5, which is negative. Sign in step (5) should be $> .$ $> .$
53. $130 \leq d \leq 144 yd$ $130 \leq d \leq 144 yd$
55. $2000 \leq M \leq 1,000,000$ $2000 \leq M \leq 1,000,000$
57. $18,000 < v < 25,000 mi/h$ $18,000 < v < 25,000 mi/h$
59. $630 \leq ω \leq 1530 r/min$ $630 \leq ω \leq 1530 r/min$
61. $5 \leq t \leq 6 h$ $5 \leq t \leq 6 h$

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Table of Contents for Exercises 17.1, page 474