course Mth 158
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3. If each side of an inequality is multiplied by a(an) NEGATIVE number, then the sense of the inequality symbol is reversed.
Assume that a 1 a. add 3 - (5 > 4) b. subtract 5 - (-3 < -4) c. multiply 3 -( 6 > 3 ) d. multiply by -2 -( -4 > -2)
21. 2x + 1 < 2 a. 2x + 2 < 5 b. 2x - 4 < -3
c. 6x + 3 < 6 d. -4x - 2 > -4
25. 4 < or equal to x < 6 (4,6) ___)_______)_____
4 6
28. x < or equal to 5 (5) ______________)_____
5
31. (2,5) 2 < or equal to x < or equal to 5 ____)_________)_______
2 5
34. (0,1) 0 < or equal to x less than or equal 1
_____)___)____
0 1
37. (-x, -3) x < -3 __)_______)________
-3 0
Fill in blank with correct inequal symbol.
40. If x < -4, then x + 4 > 0
43. If x > or equal to -4, then 3x > or equal to -12
46. If x > -2 , then -4x < 8
49. If 2x > 6, then x > 3
52. If -1/4 x > 1, then x > or equal to -4
55. 1 - 2x < or equal to 3
- 2x < or equal to 2 x > or equal to -1
___)___)______
-1 0
58. ???
61. -2 (x+3) < 8 x + 3 > -4 x > -7
___)_____________)_______
-7 0
64. 8 - 4(2-x) < or equal to -2X
8 - 4(8-4x) < or equal to -2x
4(4x) < or equal to -2x
16x < or equal to -2x
67. x/2 > or equal to 1 - x/4
2x > or equal to 4 - x
3x > or equal to x > or equal to 4/3
x > or equal to 4/3 _______}_______
4/3
70. 4 < or equal to 2x + 2 < or equal to 10
4 < or equal to 4x < or equal to 10
73. -3 < 2x-1/4 < 0
-12 < 2x - 1 < 0
-11 < 2x < 1 11/2 < x < 1/2
-11/2 and 1/2 ___)________________)____
-11/2 1/2
76. ????
79. x(4x + 3) < or equal to (2x + 1)^2
4x^2 + 3x < or equal to 4x^2 + 4x + 1
3x < or equal to 4x + 1
82. ???
85. 0 < 2/x < 3/5
10 < 3x
10/3 < x
x > 10/3 _____)_________________
10/3
88. ???
Find a and b
91. If 2 < x < 3, then a < -4x < b
-12 < -4x < -8
a = -12 b = -8
94. ???
97. If 6 < 3x < 12, then a < x^2 , b
2 < x < 4 4 < x^2 < 16
a - 4 b = 14
100. ????
103. Metropolitan Life Insurance Company reported that an average 25 yr. old male in 1996 could expect to live at least 48.4 more years and an average 25 year old female in 1996 could expect to live at least 54.7 more years.
a. to what age can an average 25 year old male expect to live? Express answer as inequal.
25 + 48.4 = 73.4 answer would be > or equal to 73.4
b. to what age can an average 25 year old female expect to live? Express your answer as an inequality.
25 + 54.7 = 79.7 > or equal to 79.7
c. Who can expect to live longer, a male or female? By how many years?
Female lives longer by 6.3 years 79.7 - 73.4 = 6.3
106. ???
109. ???
112. ???
115. If a < b, show that a < a+b/2 < b
The number a+b/2 is called the arithemetic mean of a and b
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Your work looks good overall; there were some questions you apparently did not understand, but in such cases you should give me a synopsis of the question and a summary of what you do and do not understand. However, as always, as long as you're doing well on the tests there is no problem.