Worked-out Problems

Chapter 3 continued
5. C; 3(0.9 7) 3(0.9) 3(7)
Distributive property
6. H; 4x and 9x are like terms because they have an identical
variable part raised to the same power.
7. A; 10 x 19
10 x 10 19 10
x 29
8. F; 8(x 2) 5(x 3) 8(x) 8(2) 5(x) 5(3)
8x 16 5x 15
3x 31
9. D; 3 8x 141
3 8x 3 141 3
8x 144
8
x
8
144
8
x 18
10. F; 7(x 5) 10 2x
7(x) 7(5) 10 2x
7x 35 10 2x
7x 25 2x
7x 25 7x 2x 7x
25 5x
25
5x
5 5
5 x
11. B; 4x 5 < 7
4x 5 5 < 7 5
4x < 12
12. G
4x
12
>
4
4
x > 3
13. D; 3x 14 > 2x 11
3x 14 3x > 2x 11 3x
14 > 5x 11
14 11 > 5x 11 11
25 > 5x
2 5
> 5 x
5 5
5 > x, orx < 5
14. The statement⏐a b⏐⏐a⏐⏐b⏐is sometimes true. For
example, let a 5 and b 3.
⏐a b⏐⏐a⏐⏐b⏐
⏐5 3⏐ ⏐5⏐⏐3⏐
⏐2⏐ 5 3
2 2 ✓
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110 Pre-Algebra
Chapter 3 Worked-Out Solution Key
14. ––CONTINUED––
Now let a 5 and b 3.
⏐a b⏐⏐a⏐⏐b⏐
⏐5 (3)⏐ ⏐5⏐⏐3⏐
⏐5 3⏐ ⏐5⏐⏐3⏐
⏐8⏐ 5 3
8 2
15. Addition has both the associative and commutative
properties, so you can start by adding $4.15 and $1.85.
Then add $2.74 to get the final total.
1.85 2.74 4.15 1.85 4.15 2.74
6.00 2.74
8.74
The total cost is $8.74.
16. Add the profit for each of the 4 months. Then divide by 4
to find the mean profit.
670 (340) 320 400
4
2 90
72.5
4
The mean profit over the 4 months is $72.50.
17. 4x 45 ≤ 180
4x 45 45 ≤ 180 45
4x ≤ 135
4 x
≤ 13 5
4 4
x ≤ 33 3 4
You can spend at most 33 3 4 minutes, or 33 minutes and
45 seconds on each of the remaining 4 subjects.
The inequality is expressed in minutes, where 180
represents the 3 hours available to do homework and
(4x 45) represents the time spent doing homework.
18. a. Total area of walls:
A 8(16) 8(14) 8(16) 8(14)
128 112 128 112
480
Total area of doors/windows:
A 3(5) 3(5) 3(7) 3(7)
15 15 21 21
72
Area to paint Area of walls Area of doors/windows
A 480 72 408
The total area needing painted is 408 square feet.
Because you want two coats, you need enough paint to
cover 2(408) 816 square feet.
You should buy two 1-gallon cans of paint and one
1-quart can of paint.
2(400) 100 800 100 900
This will paint 900 square feet.
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