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1.6 Exercise Set

Solve and graph the solution set.

1. $4 x - 3 > 2 x + 7$ $4 x - 3 > 2 x + 7$
2. $8 x + 1 \geq 5 x - 5$ $8 x + 1 \geq 5 x - 5$
3. $x + 6 < 5 x - 6$ $x + 6 < 5 x - 6$
4. $3 - x < 4 x + 7$ $3 - x < 4 x + 7$
5. $4 - 2 x \leq 2 x + 16$ $4 - 2 x \leq 2 x + 16$
6. $3 x - 1 > 6 x + 5$ $3 x - 1 > 6 x + 5$
7. $14 - 5 y \leq 8 y - 8$ $14 - 5 y \leq 8 y - 8$
8. $8 x - 7 < 6 x + 3$ $8 x - 7 < 6 x + 3$
9. $7 x - 7 > 5 x + 5$ $7 x - 7 > 5 x + 5$
10. $12 - 8 y \geq 10 y - 6$ $12 - 8 y \geq 10 y - 6$
11. $3 x - 3 + 2 x \geq 1 - 7 x - 9$ $3 x - 3 + 2 x \geq 1 - 7 x - 9$
12. $5 y - 5 + y \leq 2 - 6 y - 8$ $5 y - 5 + y \leq 2 - 6 y - 8$
13. $- \frac{3}{4} x \geq - \frac{5}{8} + \frac{2}{3} x$ $- \frac{3}{4} x \geq - \frac{5}{8} + \frac{2}{3} x$
14. $- \frac{5}{6} x \leq \frac{3}{4} + \frac{8}{3} x$ $- \frac{5}{6} x \leq \frac{3}{4} + \frac{8}{3} x$
15. $4 x (x - 2) < 2 (2 x - 1) (x - 3)$ $4 x (x - 2) < 2 (2 x - 1) (x - 3)$
16. $(x + 1) (x + 2) > x (x + 1)$ $(x + 1) (x + 2) > x (x + 1)$

Find the domain of the function.

17. $h (x) = \sqrt{x - 7}$ $h (x) = \sqrt{x - 7}$
18. $g (x) = \sqrt{x + 8}$ $g (x) = \sqrt{x + 8}$
19. $f (x) = \sqrt{1 - 5 x} + 2$ $f (x) = \sqrt{1 - 5 x} + 2$
20. $f (x) = \sqrt{2 x + 3} - 4$ $f (x) = \sqrt{2 x + 3} - 4$
21. $g (x) = \frac{5}{\sqrt{4 + x}}$ $g (x) = \frac{5}{\sqrt{4 + x}}$
22. $h (x) = \frac{x}{\sqrt{8 - x}}$ $h (x) = \frac{x}{\sqrt{8 - x}}$

Solve and write interval notation for the solution set. Then graph the solution set.

23. $- 2 \leq x + 1 < 4$ $- 2 \leq x + 1 < 4$
24. $- 3 < x + 2 \leq 5$ $- 3 < x + 2 \leq 5$
25. $5 \leq x - 3 \leq 7$ $5 \leq x - 3 \leq 7$
26. $- 1 < x - 4 < 7$ $- 1 < x - 4 < 7$
27. $- 3 \leq x + 4 \leq 3$ $- 3 \leq x + 4 \leq 3$
28. $- 5 < x + 2 < 15$ $- 5 < x + 2 < 15$
29. $- 2 < 2 x + 1 < 5$ $- 2 < 2 x + 1 < 5$
30. $- 3 \leq 5 x + 1 \leq 3$ $- 3 \leq 5 x + 1 \leq 3$
31. $- 4 \leq 6 - 2 x < 4$ $- 4 \leq 6 - 2 x < 4$
32. $- 3 < 1 - 2 x \leq 3$ $- 3 < 1 - 2 x \leq 3$
33. $- 5 < \frac{1}{2} (3 x + 1) < 7$ $- 5 < \frac{1}{2} (3 x + 1) < 7$
34. $\frac{2}{3} \leq - \frac{4}{5} (x - 3) < 1$ $\frac{2}{3} \leq - \frac{4}{5} (x - 3) < 1$
35. $3 x \leq - 6 or x - 1 > 0$ $3 x \leq - 6 or x - 1 > 0$
36. $2 x < 8 or x + 3 \geq 10$ $2 x < 8 or x + 3 \geq 10$
37. $2 x + 3 \leq - 4 or 2 x + 3 \geq 4$ $2 x + 3 \leq - 4 or 2 x + 3 \geq 4$
38. $3 x - 1 < - 5 or 3 x - 1 > 5$ $3 x - 1 < - 5 or 3 x - 1 > 5$
39. $2 x - 20 < - 0.8 or 2 x - 20 > 0.8$ $2 x - 20 < - 0.8 or 2 x - 20 > 0.8$
40. $5 x + 11 \leq - 4 or 5 x + 11 \geq 4$ $5 x + 11 \leq - 4 or 5 x + 11 \geq 4$
41. $x + 14 \leq - \frac{1}{4} or x + 14 \geq \frac{1}{4}$ $x + 14 \leq - \frac{1}{4} or x + 14 \geq \frac{1}{4}$
42. $x - 9 < - \frac{1}{2} or x - 9 > \frac{1}{2}$ $x - 9 < - \frac{1}{2} or x - 9 > \frac{1}{2}$
43. World Rice Production. The three countries with the most rice production are China, India, and Indonesia. The equation $y = 9.06 x + 410.81$ $y = 9.06 x + 410.81$ provides a good estimate of world rice production in millions of metric tons, where x is the number of years after 1980. (Source: www.geohive.com) For what years will world rice production exceed 820 million metric tons?
44. Social Security Disability. The equation $y = 0.326 x + 7.148$ $y = 0.326 x + 7.148$ can be used to estimate the number of people, in millions, collecting Social Security disability payments, where x is the number of years after 2007 (Source: Social Security Administration). For what years will the number of people collecting disability payments be more than 12 million?
45. Moving Costs. Acme Movers charges $200 plus $45 per hour to move a household across town. Leo’s Movers charges $65 per hour. For what lengths of time does it cost less to hire Leo’s Movers?
46. Investment Income. Jalyn plans to invest $12,000, part at 4% simple interest and the rest at 6% simple interest. What is the most that she can invest at 4% and still be guaranteed at least $650 in interest per year?
47. Investment Income. Dillon plans to invest $7500, part at 4% simple interest and the rest at 5% simple interest. What is the most that he can invest at 4% and still be guaranteed at least $325 in interest per year?
48. Investment Income. A foundation invests $150,000 at simple interest, part at 7%, twice that amount at 4%, and the rest at 5.5%. What is the most that the foundation can invest at 4% and be guaranteed at least $7575 in interest per year?
49. Investment Income. A university invests $1,400,000 at simple interest, part at 5%, half that amount at 3.5%, and the rest at 5.5%. What is the most that the university can invest at 3.5% and be guaranteed at least $68,000 in interest per year?
50. Income Plans. Karen can be paid in one of two ways for selling insurance policies:
- Plan A: A salary of $750 per month, plus a commission of 10% of sales;
- Plan B: A salary of $1000 per month, plus a commission of 8% of sales in excess of $2000.
For what amount of monthly sales is plan A better than plan B if we can assume that Karen’s sales are always more than $2000?
51. Income Plans. Curt can be paid in one of two ways for selling furniture:
- Plan A: A salary of $900 per month, plus a commission of 10% of sales;
- Plan B: A salary of $1200 per month, plus a commission of 15% of sales in excess of $8000.
For what amount of monthly sales is plan B better than plan A if we can assume that Curt’s sales are always more than $8000?
52. Income Plans. Jeanette can be paid in one of two ways for painting a house:
- Plan A: $200 plus $12 per hour;
- Plan B: $20 per hour.
Suppose a job takes n hours to complete. For what values of n is plan A better for Jeanette?

Skill Maintenance

Vocabulary Reinforcement

In each of Exercises 47–50, fill in the blank(s) with the correct term(s). Some of the given choices will not be used; others will be used more than once.

constant
function
any
midpoint formula
y-intercept
range
domain
distance formula
exactly one
identity
x-intercept

53. A(n) ____________ is a correspondence between a first set, called the ____________, and a second set, called the ____________, such that each member of the ____________ corresponds to ____________ member of the ____________. [1.2]
54. The ____________ is $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ . [1.1]
55. A(n) ____________ is a point (a, 0). [1.1]
56. A function f is a linear function if it can be written as $f (x) = m x + b$ $f (x) = m x + b$ , where m and b are constants. If $m = 0$ $m = 0$ , the function is a(n) ____________ function $f (x) = b$ $f (x) = b$ . If $m = 1$ $m = 1$ and $b = 0$ $b = 0$ , the function is the ____________ function $f (x) = x$ $f (x) = x$ . [1.3]

Synthesis

Solve.

57. $2 x \leq 5 - 7 x < 7 + x$ $2 x \leq 5 - 7 x < 7 + x$
58. $x \leq 3 x - 2 \leq 2 - x$ $x \leq 3 x - 2 \leq 2 - x$
59. $3 y < 4 - 5 y < 5 + 3 y$ $3 y < 4 - 5 y < 5 + 3 y$
60. $y - 10 < 5 y + 6 \leq y + 10$ $y - 10 < 5 y + 6 \leq y + 10$

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Table of Contents for 1.6 Exercise Set

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Table of Contents for
1.6 Exercise Set