Worked-out Problems

Chapter 3 continued
6. 5 < n
5 < 4, so 4 is a solution.
7. x 2 > 3
x 2 2 > 3 2
x > 5
6
Check: x 2 > 3
2 2 ? > 3
0 > 3 ✓
8. 1 ≥ x 9
1 9 ≥ x 9 9
10 ≥ x, orx ≤ 10
Check: 1 ≥ x 9
1 ? ≥ 8 9
1 ≥ 1 ✓
9. x 4 < 3
x 4 4 < 3 4
x < 1
3
5
0 2 4 6 8 10
2
Check: x 4 < 3
2 4 ? < 3
2 < 3 ✓
10. x 3 > 7
x 3 4 > 7 3
x > 4
0 1 2 3 4 5
Check: x 3 > 7
6 3 ? > 7
9 > 7 ✓
11. (1) Let x the number of hours the pilot must log.
Hours pilot
must log
x 250 ≥ 1000
(2) x 250 250 ≥ 1000 250
x ≥ 750
0
4
1
3
0 1 2 3
500
2
1
Hours
logged
1000
0
12
6
≥
Minimum
hours needed
1500
Check: x 250 ≥ 1000
753 250 ? ≥ 1000
1003 ≥ 1000 ✓
(3) The pilot must log at least 750 more hours to become
a pilot astronaut.
3.4 Practice and Problem Solving (pp. 141–142)
12. Let t the weight a forklift can raise, in pounds.
t ≤ 2500
13. Let s the speed limit, in miles per hour.
s ≤ 55
14. Let w the weight a truck can tow, in pounds.
w ≤ 7700
15. Let h your height, in inches.
h ≥ 48
16. Let s the savings on DVD players, in dollars.
s ≤ 50
17. x > 1 18. x ≥ 5 19. x ≤ 6 20. x < 20
21. x 4 < 5
x 4 4 < 5 4
x < 1
3 2 1
22. m 8 ≥ 12
m 8 8 ≥ 12 8
m ≥ 4
23. 11 < y 5
11 5 < y 5 5
16 < y, ory > 16
24 20 16 12 8
24. 8 ≥ d 7
8 7 ≥ d 7 7
1 ≥ d, ord ≤ 1
3
2
25. 45 > g 16
45 16 > g 16 16
29 > g, org < 29
26. z 15 > 72
z 15 15 > 72 15
z > 87
27. f 1 ≥ 8
f 1 1 ≥ 8 1
f ≥ 9
15 12
1
31 29 27 25
83 84 85
9
86 87 88 89
6
0 1 2 3
0 1 2 3 4 5
0 1 2 3
3
4
6
0
0 3
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Chapter 3
Pre-Algebra 91
Worked-Out Solution Key