Worked-out Problems

Chapter 3 continued
22. Let m the number of movie rentals.
Option 1: Pay per movie
Cost of
movie rental
p
4m
Option 2: One-time membership fee
Cost of Number
Membership
movie p of movie 10 1.50m
fee
rental rentals
10 1.50m < 4m
10 1.50m 1.50m < 4m 1.50m
10 < 2.50m
10
< 2 .50m
2 .50
2.50
4 < m, orm > 4
The cost of the membership will be less than the
cost of renting movies without the membership
after 4 movie rentals.
23. Let d the number of days the commercial is aired.
Production Cost Number
p < Budget
cost per day of days
500 50d ≤ 15,000
500 50d 500 ≤ 15,000 500
50d ≤ 14,500
5 0d
≤ 14 ,500
50
50
d ≤ 290
The company can afford to run the commercial not more
than 290 days.
24. Sample answer: In the fourth statement, the direction of
the inequality symbol should have been reversed because
each side was divided by a negative number.
4x > 6x 3
4x 6x > 6x 3 6x
2x > 3
2x
3
<
2
2
x < 3 2
Number of
movie rentals
25. 4(5 3b) > 4b 4
20 12b > 4b 4
20 12b 4b > 4b 4 4b
20 16b > 4
20 16b 20 > 4 20
16b > 16
16
1
b
6
< 1
6
16
b < 1
26. x 2
> 4
3
3 p x 2
> 3 p 4
3
x 2 > 12
x 2 2 > 12 2
x > 14
0 7 14 21 28 35
27. 3y 5 < 2(17 5y)
3y 5 < 34 10y
3y 5 10y < 34 10y 10y
13y 5 < 34
13y 5 5 < 34 5
13y < 39
1
1 3y
< 3 9
13
13
y < 3
28. x 5
≤ 2
3
3 p x 5
≤ 3 p 2
3
x 5 ≤ 6
x 5 5 ≤ 6 5
x ≤ 1
3
2
0 1 2
1
29. 5s 8
≥ 22
4
4 p 5s 8
≥ 4(22)
4
5s 8 ≥ 88
5s 8 8 ≥ 88 8
5s ≥ 80
5
s
5
≤ 80
5
0 4 8
s ≤ 16
12 16 20
42
3 4 5
0 1 2 3
24
3
2
1
0 1 2
3
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Chapter 3
Pre-Algebra 101
Worked-Out Solution Key