College Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th edition — by Raymond Barnett, Michael Ziegler | Solutions Manual (Chapter 1-15)

Solutions Manual
for
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College Mathematics for
Business, Economics, Life
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Sciences, and Social Sciences,
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14th edition By Raymond
Barnett, Michael Ziegler
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(All Chapters 1-15, 100%
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Original
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Verified, A+ Grade)
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, 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
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6. Linear Programming: The Simplex Method

7. Logic, Sets, and Counting

8. Probability
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9. Limits and the Derivative
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10. Additional Derivative Topics

11. Graphing and Optimization

12. Integration
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13. Additional Integration Topics

14. Multivariable Calculus
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15. Markov Chains
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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
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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
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x = −2

10. −6  x  −1 12. x  9 or 9  x  
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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)
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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
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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)
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–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
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4x = 16
x=4

28. x − 2 ≥ 2(x − 5) y
−
y
=
1
30.
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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




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, 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
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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
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−18 ≤ 2t ≤ 18 −2x = 3y − 24
−9 ≤ t ≤ 9 or [–9, 9]. 3y – 24 3
x= = − y + 12
–2 2
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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
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5
9
F = C + 32
5
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44. –10 8 – 3u –6
–18 –3u –14
18 ? 3u ? 14
14
6 ?u?
3
14
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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
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and hence a − b > 0.

48. Let x = number of quarters in the meter. Then
100 − x = number of dimes in the meter.
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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.



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