{3, 5}, {3, 7}, {5, 7}, {1, 3, 5}, {1,3, 7}, {1, 5, 7}, {3, 5, 7},
{1,3, 5, 7} 57. B’ = {1,2, 3, 5, 7, 15} 58.no 59. l < b- n < 3 61. 7 > r 62. = 63. > 64. >
Lesson 3-7 pp. 207-213
Go t It? 1. n = 3 and n = - 3
-—I—#—f------- 1 ----l-# H--------1— * -
-4 -2 0 2 4 6 - The 80 represents your friend's starting distance from
you. The 5 represents your friend's constant speed of
5 ft/s. She is 60 ft away at 4 s and 28 s. 3. no solution - x > 0.5 or x < -4.5
-8 -6 -4 -2 0 2
5a. \ w - 321 < 0.05; 31.95 < 32.05 b. No; 213 is
part of the absolute value expression. You cannot add 213
until after you write the absolute value inequality as a
compound inequality.
Lesso n Ch eck 1. x = 5 o r x = - 5 • — i— i— i—
-5 0 5- n = 7 or n = -7 -*—•— i— i— i—•-+
-7 0 7
3.f=3orf=-3 •—i—i—i—
-3 0 3 - -2 < h < 8 ’ (D i 1— i--- 1 cd i
- 2 0 2 4 6 8
- x<-3o rx>-1 < i •— i— •— i-----t—
-4 -3 - 2 - 1 o 1 - 2; there are two values on a number line that are
the same distance from 0. 7. The absolute value cannot
be equal to a negative number since distance from 0 on
a number line must be nonnegative. 8. Answers may
vary. Sample: The equation is set equal to 2 and -2. The
first inequality is set to be < 2 and > -2. The second
inequality is set to be > 2 or < -2.
Ex er ci ses 9. b = - ^ o r b = j
-—i—i i—i—i i—i—*- - n = 4 or n =-4 < • i—i—i—i—i—i—i • >
-4 -2 0 2 4
13.x = 8orx=-8 < m i— i— i— i— i— i— i • >
-8 - 4 0 4 8 - m = 3 or m = - 3 - —i i—i—i—i—i » i—
-4 -2 0 2 4 - r=13orr = 3 19. g = -1 o rg = -5 21. no
solution 23. v= 6 or v= 0 25. f= 1 .5 or f= -2 - y = 3 or y = 0 29. no solution 31. no solution
- -5<x<5 -—i— i—®—i— i—h-0 i—i—-
-10 -5 0 5 10 - y < —11 o r y > - 5 I-----•--- 1 ---- 1 ---• i
-13 -11 -9 -7 -5 -3 - 4 < p £ 10 i • ---- 1 ----1— •----1— -
2 4 6 8 10 12 - t < -3 or t > | 7
-3 3
« i o i 1 -----e—i---- 1 —
- 4 —2 0 2 4 6
- t £ -2.4 or t s 4 _2.4
I-----M----- 1 --- 1 -----•---1—
-4 -2 0 2 4 6 - — 4<\/<5 » >----i----- 1 ----- 1 --i m i—
- 4 - 2 0 2 4 6
- -1 1 < f< 2 -11 2
-— r*— i------ 1 -------i-»-i---- 1 —
- 1 2 - 8 - 4 0 4 8
- any length between 89.95 cm and 90.05 cm, inclusive
- d= 9 or d= -9 51. no solution 53. y= 3.4 or
y = -0.6 55. c=8.2 or c = -0.2 57. -6\<n<6\ - -8 < m < 4 61. 49°F < T< 64°F 63. The 200
represents your friend's starting distance from you. The 18
represents your friend's constant speed of 18 ft/s.
t = 4{| s and 17^ s 65. -1 < y + 7 < 1, -8 <y < -6 - Answers may vary. Sample: To be more than 1 unit
away from - 5 on a number line means x + 5 > 1 or
x+ 5 < —1. 69a. between 193.74 g and 209.26 g,
inclusive b. Yes; answers may vary. Sample: Some nickels
could weigh more and some could weigh less, and their
average could be the official amount. 71. |x| < 4 - |x — 6 1 > 2 75. between 89.992 mm and
90.008 mm, inclusive 77. 2 79. 3 81. always - 4.265 85. 5 87. 120 88. -282 < e < 20,320
- 36.9 < T< 37.5 90. 2x+ 10 91. -3y+21
- 4€ + 5 93. -m + 12 94. A = {x|x is a whole
number, x < 10} 95. B = {x|x is an odd integer,
1<x<7} 96. C= {-14,-12,-10,-8,-6} - D= { 8 , 9, 10, 12, 14, 15, 16}
Lesson 3-8 pp. 214-220
Got It? 1a. P={0, 1, 2, 3, 4}; Q= {2, 4};
P U 0 = {0, 1, 2, 3, 4} b. Answers may vary. Sample: If
B C A, then A U B will contain the same elements as
A. 2a. A n 6 = {2, 8 } b. A n C = 0 c. C fl B =
{5, 7} 3. A and E 4. 10 5a. {x|x>3} Pi {x|x< 6 }
b. {x|x< -2 } U {x|x> 5}
Lesson Check 1. XU Y= {1, 2, 3, 4, 5, 6 , 7, 8 , 9, 10}- X PI Y= {2, 4, 6, 8, 10} 3. X D Z=0 4. YU Z =
{1 , 2, 3, 4, 5, 6 , 7, 8, 9, 10} 5. 31 people 6. A U B
contains more elements because it contains all the
elements in both sets. 7. The union of sets is the set that
contains all elements of each set. The intersection of sets is
the set of elements that are common to each set. 8. true
9. false
Exercises 11. A U C= {1, 2, 3, 4, 5, 7, 10}
13. S U C = {0, 2, 4, 5, 6 , 7, 8 , 10} 15. CU D = {1, 2,
3, 5, 7, 9, 10} 17. A fl C = 0 19. B FT C= {2}
21. C fl D= {5, 7}
c
Po w er A lg eb r a.co m : Selected Answ ers 873