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Building Skills

9. $0 . \bar{3}$ $0 . \bar{3}$ repeating
10. $0 . \bar{6}$ $0 . \bar{6}$ repeating
11. $- 0.8$ $- 0.8$ terminating
12. $- 0.25$ $- 0.25$ terminating
13. $0 . \bar{27}$ $0 . \bar{27}$ repeating
14. $0 . \bar{3}$ $0 . \bar{3}$ repeating
15. $3.1 \bar{6}$ $3.1 \bar{6}$ repeating
16. $2.7 \bar{3}$ $2.7 \bar{3}$ repeating
17. $\frac{15}{4}$ $\frac{15}{4}$
18. $- \frac{47}{20}$ $- \frac{47}{20}$
19. $- \frac{16}{3}$ $- \frac{16}{3}$
20. $\frac{29}{3}$ $\frac{29}{3}$
21. $\frac{211}{99}$ $\frac{211}{99}$
22. $\frac{320}{99}$ $\frac{320}{99}$
23. $\frac{2239}{495}$ $\frac{2239}{495}$
24. $\frac{14, 093}{9900}$ $\frac{14, 093}{9900}$
25. Rational
26. Rational
27. Rational
28. Rational
29. Rational
30. Rational
31. Irrational
32. Irrational
33. 2 and 11
34. 0, 2, and 11
35. $- 19, - \frac{12}{3} (or - 4), 0, 2,$ $- 19, - \frac{12}{3} (or - 4), 0, 2,$ and 11
36. $- 19, - \frac{12}{3}, 0, 2, \frac{17}{4}, 11$ $- 19, - \frac{12}{3}, 0, 2, \frac{17}{4}, 11$
37. $- \sqrt{3}$ $- \sqrt{3}$ and $\sqrt{10}$ $\sqrt{10}$
38. All numbers in the set A are real numbers
39. base 10, exponent 3, 1000
40. base 5, exponent 4, 625
41. base $\frac{2}{3},$ $\frac{2}{3},$ exponent 3, $\frac{8}{27}$ $\frac{8}{27}$
42. base $\frac{5}{2},$ $\frac{5}{2},$ exponent 4, $\frac{625}{16}$ $\frac{625}{16}$
43. base $- 2,$ $- 2,$ exponent 3, $- 8$ $- 8$
44. base $- \frac{1}{2},$ $- \frac{1}{2},$ exponent 4, $\frac{1}{16}$ $\frac{1}{16}$
45. base 3, exponent 4, 162
46. base $\frac{1}{3}$ $\frac{1}{3}$ , exponent 3, $\frac{5}{27}$ $\frac{5}{27}$
47. base 3, exponent 4, $- 162$ $- 162$
48. base $- 2,$ $- 2,$ exponent 4, $- 48$ $- 48$
49. base $- 2,$ $- 2,$ exponent 5, 96
50. base $- 3,$ $- 3,$ exponent 2, $- 45$ $- 45$
51. $3 > - 2$ $3 > - 2$
52. $- 3 < - 2$ $- 3 < - 2$
53. $\frac{1}{2} \geq \frac{1}{2}$ $\frac{1}{2} \geq \frac{1}{2}$
54. $x < x + 1$ $x < x + 1$
55. $5 \leq 2 x$ $5 \leq 2 x$
56. $x - 1 > 2$ $x - 1 > 2$
57. $- x > 0$ $- x > 0$
58. $x < 0$ $x < 0$
59. $2 x + 7 \leq 14$ $2 x + 7 \leq 14$
60. $2 x + 3 \leq 5$ $2 x + 3 \leq 5$
61. $=$ $=$
62. $<$ $<$
63. $<$ $<$
64. $=$ $=$
65. ${- 4, - 3, - 2, 1, 2, 3, 4}$ ${- 4, - 3, - 2, 1, 2, 3, 4}$
66. ${0, 2, 4}$ ${0, 2, 4}$
67. ${- 4, - 2, 0, 2}$ ${- 4, - 2, 0, 2}$
68. ${- 4, 3, 2, - 1, 0, 1, 2, 3, 4}$ ${- 4, 3, 2, - 1, 0, 1, 2, 3, 4}$
69. ${- 4, - 3, - 2, 0, 2, 4}$ ${- 4, - 3, - 2, 0, 2, 4}$
70. ${- 3, 0, 2, 4}$ ${- 3, 0, 2, 4}$
71. ${- 4, - 3, - 2, 0, 2}$ ${- 4, - 3, - 2, 0, 2}$
72. ${- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4}$ ${- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4}$
73. $(- 2, 5), [1, 3]$ $(- 2, 5), [1, 3]$
74. $[1, 7], (3, 5)$ $[1, 7], (3, 5)$
75. $(- 6, 10), \emptyset$ $(- 6, 10), \emptyset$
76. $(- \infty, \infty), \emptyset$ $(- \infty, \infty), \emptyset$
77. $(- \infty, \infty), [2, 5)$ $(- \infty, \infty), [2, 5)$
78. $(- 2, \infty), (0, \infty)$ $(- 2, \infty), (0, \infty)$
79. $(- \infty, \infty), [- 1, 3) \cup [5, 7]$ $(- \infty, \infty), [- 1, 3) \cup [5, 7]$
80. $(- \infty, 2] \cup (6, \infty), [- 3, 0]$ $(- \infty, 2] \cup (6, \infty), [- 3, 0]$
81. 4
82. $- 17$ $- 17$
83. $\frac{5}{7}$ $\frac{5}{7}$
84. $\frac{3}{5}$ $\frac{3}{5}$
85. $5 - \sqrt{2}$ $5 - \sqrt{2}$
86. $5 - \sqrt{2}$ $5 - \sqrt{2}$
87. $2 - \sqrt{3}$ $2 - \sqrt{3}$
88. $π - 3$ $π - 3$
89. 1
90. $- 1$ $- 1$
91. 2
92. 3
93. $| 3 - 8 | = 5$ $| 3 - 8 | = 5$
94. $| 2 - 14 | = 12$ $| 2 - 14 | = 12$
95. $| - 6 - 9 | = 15$ $| - 6 - 9 | = 15$
96. $| - 12 - 3 | = 15$ $| - 12 - 3 | = 15$
97. $| - 20 - (- 6) | = 14$ $| - 20 - (- 6) | = 14$
98. $| - 14 - (- 1) | = 13$ $| - 14 - (- 1) | = 13$
99. $| \frac{22}{7} - (- \frac{4}{7}) | = \frac{26}{7}$ $| \frac{22}{7} - (- \frac{4}{7}) | = \frac{26}{7}$
100. $| \frac{16}{5} - (- \frac{3}{5}) | = \frac{19}{5}$ $| \frac{16}{5} - (- \frac{3}{5}) | = \frac{19}{5}$
101. $- 3 < x \leq 1$ $- 3 < x \leq 1$
102. $- 6 \leq x < - 2$ $- 6 \leq x < - 2$
103. $x \geq - 3$ $x \geq - 3$
104. $x \geq 0$ $x \geq 0$
105. $x \leq 5$ $x \leq 5$
106. $x \leq - 1$ $x \leq - 1$
107. $- \frac{3}{4} < x < \frac{9}{4}$ $- \frac{3}{4} < x < \frac{9}{4}$
108. $- 3 < x < - \frac{1}{2}$ $- 3 < x < - \frac{1}{2}$
109. $4 x + 4$ $4 x + 4$
110. $- 6 + 3 x$ $- 6 + 3 x$
111. $5 x - 5 y + 5$ $5 x - 5 y + 5$
112. $6 x + 10 - 2 y$ $6 x + 10 - 2 y$
113. $- 5; \frac{1}{5}$ $- 5; \frac{1}{5}$
114. $\frac{2}{3}; - \frac{3}{2}$ $\frac{2}{3}; - \frac{3}{2}$
115. 0; No reciprocal
116. $- 1.7; \frac{10}{17}$ $- 1.7; \frac{10}{17}$
117. Additive inverse
118. Additive inverse
119. Multiplicative identity
120. Multiplicative identity
121. Multiplicative associative
122. Multiplicative associative
123. Multiplicative inverse
124. Multiplicative inverse
125. Additive identity
126. Additive identity
127. Additive associative
128. Additive, commutative, and associative
129. $\frac{29}{15}$ $\frac{29}{15}$
130. $\frac{29}{20}$ $\frac{29}{20}$
131. $\frac{67}{35}$ $\frac{67}{35}$
132. $\frac{59}{12}$ $\frac{59}{12}$
133. $\frac{17}{15}$ $\frac{17}{15}$
134. $\frac{34}{45}$ $\frac{34}{45}$
135. $- \frac{11}{40}$ $- \frac{11}{40}$
136. $\frac{27}{40}$ $\frac{27}{40}$
137. $- \frac{8}{99}$ $- \frac{8}{99}$
138. $\frac{1}{24}$ $\frac{1}{24}$
139. $- \frac{1}{10}$ $- \frac{1}{10}$
140. $\frac{1}{12}$ $\frac{1}{12}$
141. $\frac{2}{9}$ $\frac{2}{9}$
142. $\frac{2}{3}$ $\frac{2}{3}$
143. $\frac{3}{2}$ $\frac{3}{2}$
144. $\frac{1}{3}$ $\frac{1}{3}$
145. $\frac{2}{3}$ $\frac{2}{3}$
146. $\frac{9}{14}$ $\frac{9}{14}$
147. 1
148. $\frac{11}{2}$ $\frac{11}{2}$
149. $\frac{1}{15}$ $\frac{1}{15}$
150. $\frac{11}{6}$ $\frac{11}{6}$
151. 11
152. $- 21$ $- 21$
153. $- 1$ $- 1$
154. 56
155. $- 6$ $- 6$
156. $\frac{43}{3}$ $\frac{43}{3}$
157. $- 13$ $- 13$
158. $- \frac{77}{5}$ $- \frac{77}{5}$
159. $\frac{62}{15}$ $\frac{62}{15}$
160. $- \frac{104}{75}$ $- \frac{104}{75}$
161. $\frac{3 x + x y}{3 y}$ $\frac{3 x + x y}{3 y}$
162. $(x + 2) (x + 3) = x^{2} + 5 x + 6$ $(x + 2) (x + 3) = x^{2} + 5 x + 6$
163. $5 (x + 3) = 5 x + 15$ $5 (x + 3) = 5 x + 15$
164. $(25 x) (4 x) = 100 x^{2}$ $(25 x) (4 x) = 100 x^{2}$
165. $x - (3 y + 2) = x - 3 y - 2$ $x - (3 y + 2) = x - 3 y - 2$
166. $2 x - (4 y - 5) = 2 x - 4 y + 5$ $2 x - (4 y - 5) = 2 x - 4 y + 5$
167. $\frac{x + y}{x} = 1 + \frac{y}{x}$ $\frac{x + y}{x} = 1 + \frac{y}{x}$
168. $\frac{x + y}{x + z} = \frac{x}{x + z} + \frac{y}{x + z}$ $\frac{x + y}{x + z} = \frac{x}{x + z} + \frac{y}{x + z}$
169. $(x + 1) (y + 1) = x y + x + y + 1$ $(x + 1) (y + 1) = x y + x + y + 1$
170. $\frac{\frac{1}{x}}{\frac{1}{y}} = \frac{y}{x}$ $\frac{\frac{1}{x}}{\frac{1}{y}} = \frac{y}{x}$

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Table of Contents for Building Skills

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Table of Contents for
Building Skills