,
,
, Chapter P Fundamental Concepts of Algebra
C6. natural 10.
3
6 + 5 (8 − 6) = 6 + 5 ( 2)
3
C7. whole = 6 + 5 (8)
C8. integers = 6 + 40 = 46
C9. rational 11. 82 − 3(8 − 2) = 64 − 3(6)
= 64 − 18 = 46
C10. irrational
12. 82 − 4 ( 8 − 3) = 64 − 4 ( 5 ) = 64 − 20 = 44
C11. rational; irrational
C12. absolute value; x, −x 5( x + 2) 5(10 + 2)
13. =
2 x − 14 2(10) − 14
C13. b + a ; ba 5(12)
=
6
C14. a + (b + c) ; ( ab)c
= 5⋅2
C15. ab + ac = 10
C16. 0; inverse; 0; identity 7( x − 3) 7(9 − 3) 7(6)
14. = = = 7 ⋅ 3 = 21
2 x − 16 2(9) − 16 2
C17. inverse; 1; identity
2x + 3y
C18. simplified 15. ; x = −2, y = 4
x +1
C19. a 2 ( −2 ) + 3 ( 4 ) −4 + 12 8
= = = = −8
−2 + 1 −1 −1
Exercise Set P.1
2x + y
16. ; x = −2 and y = 4
1. 7 + 5(10) = 7 + 50 = 57 xy − 2 x
2 ( −2 ) + 4 −4 + 4 0
= = =0
2. 8 + 6 ( 5 ) = 8 + 30 = 38 ( −2 )( 4 ) − 2 ( −2 ) −8 + 4 4
3. 6(3) − 8 = 18 − 8 = 10 5 5
17. C= (50 − 32) = (18) = 10
9 9
4. 8 ( 3) − 4 = 24 − 4 = 20 50°F is equivalent to 10°C.
5. 82 + 3(8) = 64 + 24 = 88 5 5 5
18. C= ( F − 32) = (86 − 32) = (54) = 30
9 9 9
6. 62 + 5 ( 6 ) = 36 + 30 = 66 86°F is equivalent to 30°C.
19. h = 4 + 60t − 16t 2 = 4 + 60(2) − 16(2) 2
7. 7 2 − 6(7) + 3 = 49 − 42 + 3 = 7 + 3 = 10
= 4 + 120 − 16(4) = 4 + 120 − 64
8. 8 − 7 ( 8 ) + 4 = 64 − 56 + 4 = 8 + 4 = 12
2 = 124 − 64 = 60
Two seconds after it is kicked, the ball’s height is
60 feet.
9. 4 + 5(9 − 7)3 = 4 + 5(2)3
= 4 + 5(8) = 4 + 40 = 44
2 Copyright © 2022 Pearson Education, Inc
,
, Chapter P Fundamental Concepts of Algebra
C6. natural 10.
3
6 + 5 (8 − 6) = 6 + 5 ( 2)
3
C7. whole = 6 + 5 (8)
C8. integers = 6 + 40 = 46
C9. rational 11. 82 − 3(8 − 2) = 64 − 3(6)
= 64 − 18 = 46
C10. irrational
12. 82 − 4 ( 8 − 3) = 64 − 4 ( 5 ) = 64 − 20 = 44
C11. rational; irrational
C12. absolute value; x, −x 5( x + 2) 5(10 + 2)
13. =
2 x − 14 2(10) − 14
C13. b + a ; ba 5(12)
=
6
C14. a + (b + c) ; ( ab)c
= 5⋅2
C15. ab + ac = 10
C16. 0; inverse; 0; identity 7( x − 3) 7(9 − 3) 7(6)
14. = = = 7 ⋅ 3 = 21
2 x − 16 2(9) − 16 2
C17. inverse; 1; identity
2x + 3y
C18. simplified 15. ; x = −2, y = 4
x +1
C19. a 2 ( −2 ) + 3 ( 4 ) −4 + 12 8
= = = = −8
−2 + 1 −1 −1
Exercise Set P.1
2x + y
16. ; x = −2 and y = 4
1. 7 + 5(10) = 7 + 50 = 57 xy − 2 x
2 ( −2 ) + 4 −4 + 4 0
= = =0
2. 8 + 6 ( 5 ) = 8 + 30 = 38 ( −2 )( 4 ) − 2 ( −2 ) −8 + 4 4
3. 6(3) − 8 = 18 − 8 = 10 5 5
17. C= (50 − 32) = (18) = 10
9 9
4. 8 ( 3) − 4 = 24 − 4 = 20 50°F is equivalent to 10°C.
5. 82 + 3(8) = 64 + 24 = 88 5 5 5
18. C= ( F − 32) = (86 − 32) = (54) = 30
9 9 9
6. 62 + 5 ( 6 ) = 36 + 30 = 66 86°F is equivalent to 30°C.
19. h = 4 + 60t − 16t 2 = 4 + 60(2) − 16(2) 2
7. 7 2 − 6(7) + 3 = 49 − 42 + 3 = 7 + 3 = 10
= 4 + 120 − 16(4) = 4 + 120 − 64
8. 8 − 7 ( 8 ) + 4 = 64 − 56 + 4 = 8 + 4 = 12
2 = 124 − 64 = 60
Two seconds after it is kicked, the ball’s height is
60 feet.
9. 4 + 5(9 − 7)3 = 4 + 5(2)3
= 4 + 5(8) = 4 + 40 = 44
2 Copyright © 2022 Pearson Education, Inc
