Solutions Manual
for
TE
College Mathematics for
Business, Economics, Life
S
Sciences, and Social Sciences,
TS
14th edition By Raymond
Barnett, Michael Ziegler
O
LU
(All Chapters 1-15, 100%
TI
Original
O
Verified, A+ Grade)
N
, Table of Content
1. Linear Equations and Graphs
2. Functions and Graphs
3. Mathematics of Finance
4. Systems of Linear Equations; Matrices
5. Linear Inequalities and Linear Programming
TE
6. Linear Programming: The Simplex Method
7. Logic, Sets, and Counting
8. Probability
S
9. Limits and the Derivative
TS
10. Additional Derivative Topics
11. Graphing and Optimization
12. Integration
O
13. Additional Integration Topics
14. Multivariable Calculus
LU
15. Markov Chains
TI
O
N
, fdsewert
1 LINEAR EQUATIONS AND GRAPHS
EXERCISE 1-1
2. 7x − 6 = 5x − 24 4. 3(x + 6) = 5 − 2(x +1)
3x +18 = 5 − 2x − 2
2x = −18
5x = −15
x = −9
x = −3
TE
2x +1 5x
6. − = 4 (multiply both sides by 6) 8. −3 x 5
3 2
2(2x +1) −15x = 24
4x + 2 −15x = 24
−11x = 22
S
x = −2
10. −6 x −1 12. x 9 or 9 x
TS
14. [−1, 5) 16. [4, )
18. −8 −4x 12 (divide the inequalities by – 4 and reverse the directions)
2 x −3 or − 3 x 2
[−3, 2)
O
m 2 x 5
20. –4= 22. <
3 3 –4 6
Multiply both sides of the equation by 3 to obtain: Multiply both sides by (−4) which will
LU
m − 12 = 2 result in changing the direction of
m = 14 the inequality as well.
–20 and simplified we have x > – 10 .
x>
6 3
24. –3y + 9 + y = 13 – 8 y 26. −3(4 − x) = 5 − (x + 1)
TI
–2 y + 9 = 13 – 8 y −12 + 3x = 5 − x − 1
6y = 4 −12 + 3x = 4 − x
4 2 12 − 12 + 3x = 12 + 4 − x
y= =
6 3 3x = 16 − x
O
4x = 16
x=4
28. x − 2 ≥ 2(x − 5) y
−
y
=
1
30.
N
x − 2 ≥ 2x − 10 4 3 2
x − 2 + 2 ≥ 2x − 10 + 2 Multiply both sides by 12:
x ≥ 2x − 8 3y − 4y = 6
− x −8 −y = 6
x≤8 y = −6
Copyright © 2019 Pearson Education, Inc.
1-1
, 1-2 CHAPTER 1: LINEARfdsewert
EQUATIONS AND GRAPHS
u 2 < u +2 34. −4 ≤ 5x + 6 < 21
32. −
2 3 3 −6 − 4 ≤ 5x < 21 − 6
u u <2+ 2 −10 ≤ 5x < 15
−
2 3 3 −2 ≤ x < 3 or [−2, 3)
u 8
<
6 3
u < 16
2 2
TE
36. −1 ≤ t + 5 ≤ 11 38. y=− x+8
3 3
2 2
−5 − 1 ≤ t ≤ 11 − 5 y–8=− x+8−8
23 3
−6 ≤ t ≤ 6 2
− x=y−8
3 3
S
−18 ≤ 2t ≤ 18 −2x = 3y − 24
−9 ≤ t ≤ 9 or [–9, 9]. 3y – 24 3
x= = − y + 12
–2 2
TS
40. y = mx + b 5
42. C= (F – 32)
y − b = mx + b − b 9
9
mx = y − b C = F − 32
y –b 5
m= 9
x 32 + C = F
O
5
9
F = C + 32
5
LU
44. –10 8 – 3u –6
–18 –3u –14
18 ? 3u ? 14
14
6 ?u?
3
14
TI
u 6 or [, 6]
3
b
46. If a and b are negative and > 1, then multiplying both sides by the negative number a we obtain b < a
a
O
and hence a − b > 0.
48. Let x = number of quarters in the meter. Then
100 − x = number of dimes in the meter.
N
Now, 0.25x + 0.10(100 − x) = 14.50 or
0.25x + 10 − 0.10x = 14.50
0.15x = 4.50
4.50
x= = 30
0.15
Thus, there will be 30 quarters and 70 dimes.
Copyright © 2019 Pearson Education, Inc.
for
TE
College Mathematics for
Business, Economics, Life
S
Sciences, and Social Sciences,
TS
14th edition By Raymond
Barnett, Michael Ziegler
O
LU
(All Chapters 1-15, 100%
TI
Original
O
Verified, A+ Grade)
N
, Table of Content
1. Linear Equations and Graphs
2. Functions and Graphs
3. Mathematics of Finance
4. Systems of Linear Equations; Matrices
5. Linear Inequalities and Linear Programming
TE
6. Linear Programming: The Simplex Method
7. Logic, Sets, and Counting
8. Probability
S
9. Limits and the Derivative
TS
10. Additional Derivative Topics
11. Graphing and Optimization
12. Integration
O
13. Additional Integration Topics
14. Multivariable Calculus
LU
15. Markov Chains
TI
O
N
, fdsewert
1 LINEAR EQUATIONS AND GRAPHS
EXERCISE 1-1
2. 7x − 6 = 5x − 24 4. 3(x + 6) = 5 − 2(x +1)
3x +18 = 5 − 2x − 2
2x = −18
5x = −15
x = −9
x = −3
TE
2x +1 5x
6. − = 4 (multiply both sides by 6) 8. −3 x 5
3 2
2(2x +1) −15x = 24
4x + 2 −15x = 24
−11x = 22
S
x = −2
10. −6 x −1 12. x 9 or 9 x
TS
14. [−1, 5) 16. [4, )
18. −8 −4x 12 (divide the inequalities by – 4 and reverse the directions)
2 x −3 or − 3 x 2
[−3, 2)
O
m 2 x 5
20. –4= 22. <
3 3 –4 6
Multiply both sides of the equation by 3 to obtain: Multiply both sides by (−4) which will
LU
m − 12 = 2 result in changing the direction of
m = 14 the inequality as well.
–20 and simplified we have x > – 10 .
x>
6 3
24. –3y + 9 + y = 13 – 8 y 26. −3(4 − x) = 5 − (x + 1)
TI
–2 y + 9 = 13 – 8 y −12 + 3x = 5 − x − 1
6y = 4 −12 + 3x = 4 − x
4 2 12 − 12 + 3x = 12 + 4 − x
y= =
6 3 3x = 16 − x
O
4x = 16
x=4
28. x − 2 ≥ 2(x − 5) y
−
y
=
1
30.
N
x − 2 ≥ 2x − 10 4 3 2
x − 2 + 2 ≥ 2x − 10 + 2 Multiply both sides by 12:
x ≥ 2x − 8 3y − 4y = 6
− x −8 −y = 6
x≤8 y = −6
Copyright © 2019 Pearson Education, Inc.
1-1
, 1-2 CHAPTER 1: LINEARfdsewert
EQUATIONS AND GRAPHS
u 2 < u +2 34. −4 ≤ 5x + 6 < 21
32. −
2 3 3 −6 − 4 ≤ 5x < 21 − 6
u u <2+ 2 −10 ≤ 5x < 15
−
2 3 3 −2 ≤ x < 3 or [−2, 3)
u 8
<
6 3
u < 16
2 2
TE
36. −1 ≤ t + 5 ≤ 11 38. y=− x+8
3 3
2 2
−5 − 1 ≤ t ≤ 11 − 5 y–8=− x+8−8
23 3
−6 ≤ t ≤ 6 2
− x=y−8
3 3
S
−18 ≤ 2t ≤ 18 −2x = 3y − 24
−9 ≤ t ≤ 9 or [–9, 9]. 3y – 24 3
x= = − y + 12
–2 2
TS
40. y = mx + b 5
42. C= (F – 32)
y − b = mx + b − b 9
9
mx = y − b C = F − 32
y –b 5
m= 9
x 32 + C = F
O
5
9
F = C + 32
5
LU
44. –10 8 – 3u –6
–18 –3u –14
18 ? 3u ? 14
14
6 ?u?
3
14
TI
u 6 or [, 6]
3
b
46. If a and b are negative and > 1, then multiplying both sides by the negative number a we obtain b < a
a
O
and hence a − b > 0.
48. Let x = number of quarters in the meter. Then
100 − x = number of dimes in the meter.
N
Now, 0.25x + 0.10(100 − x) = 14.50 or
0.25x + 10 − 0.10x = 14.50
0.15x = 4.50
4.50
x= = 30
0.15
Thus, there will be 30 quarters and 70 dimes.
Copyright © 2019 Pearson Education, Inc.
