Worked-out Problems

Chapter 3 continued
4. 3x 2x 25
5x 25
5 x
2 5
5 5
x 5
Check: 3x 2x 25
3(5) 2(5) 25
25 25 ✓
5. 21 4x 9 x
21 3x 9
21 9 3x 9 9
30 3x
3 0
3 x
3 3
10 x
Check: 21 4x 9 x
21 4(10) 9 10
21 21 ✓
6. 3(x 1) 6
3x 3 6
3x 3 3 6 3
3x 3
3 x
3 3 3
x 1
Check: 3(x 1) 6
3(1 1) 6
6 6 ✓
7. 16 8(x 1)
16 8x 8
16 8 8x 8 8
24 8x
2 4
8 x
8 8
3 x
Check: 16 8(x 1)
16 8(3 1)
16 16 ✓
8. 5 2(x 2) 19
5 2x 4 19
1 2x 19
1 2x 1 19 1
2x 18
2 x
1 8
2 2
x 9
––CONTINUED––
8. ––CONTINUED––
Check: 5 2(x 2) 19
5 2(9 2) 19
19 19 ✓
9. (1) P 2l 2w
28 2(10) 2(x 2)
(2) 28 20 2x 4
28 24 2x
28 24 24 2x 24
4 2x
4 2 2 x
2
2 x
(3) Width x 2 2 2 4
The width is 4 units.
(4) Check: P 2l 2w 2(10) 2(4) 20 8 28
The solutions checks.
3.2 Practice and Problem Solving (pp. 127–129)
10. Sample answer: The distributive property was not
applied correctly.
Distribute the 2 to the entire quantity.
2(5 n) 2
10 2n 2
10 2n 10 2 10
2n 12
n 6
11. 13t 7 10t 2
3t 7 2
3t 7 7 2 7
3t 9
3 t
9 3 3
t 3
Check: 13t 7 10t 2
13(3) 7 10(3) 2
2 2 ✓
12. 22 4y 14 0
8 4y 0
8 4y 8 0 8
4y 8
4 y
8
4 4
y 2
Check: 22 4y 14 0
22 4(2) 14 0
0 0 ✓
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Chapter 3
Pre-Algebra 75
Worked-Out Solution Key