Worked-out Problems

Chapter 3 continued
4. No. Sample answer: 2x > 6
2x
6
<
2
2
x < 3
Thus, x < 3 and x > 3 have different solutions.
So, 2x > 6 and x > 3 are not equivalent inequalities.
5. Let s the cost of a jar of sauce.
Total Cost of Jars of Cost of a
p
cost spaghetti sauce jar of sauce
6.49 1.59 2s
6.49 1.59 1.59 2s 1.59
4.90 2s
4. 90 2s
2 2
2.45 2s
One jar of sauce costs $2.45.
6. 17h 47 6h 160
23h 47 160
23h 47 47 160 47
23h 207
2 3h
2 07
23
23
h 9
Check: 17h 47 6h 160
17(9) 47 6(9) 160
160 160 ✓
7. 2(4p 8) 128
8p 16 128
8p 16 16 128 16
8p 112
8 p
11 2
8 8
p 14
Check: 2(4p 8) 128
2[4(14) 8] 128
128 128 ✓
8. 6(w 4) 18 30
6w 24 18 30
6w 6 30
6w 6 6 30 6
6w 36
6 w 36
6 6
w 6
Check: 6(w 4) 18 30
6(6 4) 18 30
30 30 ✓
9. 11t 14 95 16t
11t 14 16t 95 16t 16t
27t 14 95
27t 14 14 95 14
27t 81
2 7t
8 1
27
27
t 3
Check: 11t 14 95 16t
11(3) 14 95 16(3)
47 47 ✓
10. 9n 64 144 17n
9n 64 17n 144 17n 17n
26n 64 144
26n 64 64 144 64
26n 208
2 6n
26
208
2
6
n 8
Check: 9n 64 144 17n
9(8) 64 144 17(8)
8 8 ✓
11. 3 2x 2(2 x)
3 2x 4 2x
3 2x 2x 4 2x 2x
3 4
No solution
12. 3(2 6b) 18b
6 18b 18b
6 18b 18b 18b 18b
6 0
No solution
13. y 11 < 23
y 11 11 < 23 11
y < 12
0 3 6 9 12 15 18
14. 15 ≥ z 9
15 9 ≥ z 9 9
6 ≥ z, orz ≤ 6
0 2 4 6 8 10 12
15. x 5 ≤ 14
x 5 5 ≤ 14 5
x ≤ 19
15 16 17 18 19 20 21
104 Pre-Algebra
Chapter 3 Worked-Out Solution Key
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