Worked-out Problems

Chapter 3 continued
2. 5x 12 < 8
Sample answer:
(1) Subtract 12 from 5x 12 12 < 8 12
each side.
(2) Simplify. 5x < 20
(3) Divide each side by 5
x
5
> 20
5
5 and reverse the
inequality symbol.
(4) Simplify. x > 4
3. 4x 1 > 1
4x 1 1 > 1 1
4x > 0
3
4 x
> 0 4 4
x > 0
Check: 4x 1 > 1
4(2) 1 ? > 1
9 > 1 ✓
4. 7 ≥ 5x 3
7 3 ≥ 5x 3 3
10 ≥ 5x
1 0
≥ 5 x
5 5
2
2
2 ≥ x, orx ≤ 2
1
1
0 1 2 3 4
Check: 7 ≥ 5x 3
7 ? ≥ 5(1) 3
7 ≥ 2 ✓
x
5. 6 < 14
2
0 1 2 3
x
6 6 < 14 6
2
x
< 20 2
x
2 p > 2(20)
2
x > 40
0 10 20 30 40 50 60
x
Check: 6 < 14
2
42
6 ? < 14
2
15 < 14 ✓
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6. 10 > 6 5
y
10 6 > 6 5
y 6
4 > 5
y
5 p 4 > 5 p 5
y
20 > y, ory < 20
Check: 10 > 6 5
y
10 ? > 6 1 5
5
10 > 9 ✓
7. 5y 2 ≤ y 34
5y 2 y ≤ y 34 y
4y 2 ≤ 34
4y 2 2 ≤ 34 2
4y ≤ 32
4 y
≤ 3 2
4 4
y ≤ 8
Check: 5y 2 ≤ y 34
5(8) 2 ? ≤ 8 34
42 ≤ 42 ✓
8. 6 y ≥ 2y 3
6 y y ≥ 2y 3 y
6 ≥ y 3
6 3 ≥ y 3 3
9 ≥ y, ory ≤ 9
3
0 5 10 15 20 25 30
0 2 4 6 8 10 12
0 3 6
Check: 6 y ≥ 2y 3
6 6 ? ≥ 2(6) 3
12 ≥ 9 ✓
9. (1) Let v the number of visits to the park.
Option 1: Not buying a season pass
Cost of Number Cost of Number
p p
admission of visits parking of visits
23v 10v 33v
(2) Option 2: Buying a season pass
Cost of
season pass
120 8v
120 8v < 33v
––CONTINUED––
Chapter 3
9 12 15
Cost of
parking
p
Number
of visits
Pre-Algebra 99
Worked-Out Solution Key