52.Concept Check Frank Capek’s grandson was asked to evaluate the following expression.Frank gave the answer as 8, but his grandson gave the answer as 14. The grandson ex-
plained that the answer is 14 because of the “Order of Process rule” which says that in a
problem like this, you proceed from right to left rather than left to right. (Note: This is a
true story.)
(a)Whose answer was correct for this expression, Frank’s or his grandson’s?
(b)Was the reasoningfor the correct answer valid? Explain.9 + 15 , 3
30 CHAPTER 1 Review of the Real Number System
Simplify each expression. Use the order of operations. See Examples 4–6.71. 72.
73. 74.
75. 76.
77. 78.
- 4 a
12 -^1 -^82
3 # 2 + 4
b- 51 - 1 - 72- 9 - 1 - 72 - 3 - 5 - 1 - 824
5 - 3 a- 5 - 9
- 7
b- 6- 9 - 11 + 3 # 7
31 - 42 + 1 - 521 - 82
23 - 2 - 6
21 - 52 + 1 - 321 - 22
- 8 + 32 - 1
A- 9 + 16 B 1 - 322
- 4 - 1
A- 5 + 4 B 1 - 222
- 5 - 1
- 12 a-
3
4
- 14 a- b - 16 # 5 , 32
2
7
b , 12 # 6 - 102
7 -
3
4
1 - 82 + 12 #
5
6
6 +
2
3
1 - 92 -
5
8
16
|- 6 - 5 | 1 - 82 + 32 1 - 6 - 32 |- 2 - 3 |, 9
6 | 4 - 5 |- 24 , 3 - 4 | 2 - 4 |+ 8 # 2
- 7 A 36 B- 1 - 221 - 32 - 8 A 64 B- 1 - 321 - 72
5 - 7 # 3 - 1 - 223 - 4 - 3 # 5 + 62
- 31522 - 1 - 221 - 82 - 91222 - 1 - 321 - 22
10 + 30 , 2 # 3 12 + 24 , 3 # 2
6 # 3 - 12 , 4 9 # 4 - 8 , 2
12 + 3 # 4 15 + 5 # 2
Evaluate each expression for ,,and. See Example 7.85. 86.
3 c+a^2
2 b- 6 c2 c+a^3
4 b+ 6 ab-c+a 4 a^3 + 2 c - 3 a^4 - 3 c3 a+b - 2 a-b b+c-aa=- 3 b= 64 c= 6Evaluate each expression for , and See Example 7.93. 94.
7 y- 5 x
2 w7 x+ 9 y
wxy-x^2 - w+ 2 x+ 3 y+z w- 6 x+ 5 y- 3 zwy- 8 x wz- 12 y xy+y^4w= 4 x=-^34 ,y=^12 , z=1.25.