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Chapter 2 Review
Section 2.1: Basic Assumptions
Simplify.
1. 2 ∙ 21 ∙ 5 ∙ 3
2. 5 + 3𝑥 + 12
3. (−3𝑟)(5𝑠)(8𝑝)
5. If 𝑥 = 𝑦, then 𝑦 = 𝑥
6. 𝑦 + 5 = 5 + 𝑦
Name the property illustrated.
4.(2𝑥)𝑦 = 2(𝑥𝑦)
Section 2.2: Addition on a Number Line
Simplify.
7. −3.2 + (−4.6) + 5.4
8. [0 + (−8)] + [−7 + (−23)]
10. −2 + 4𝑥 + 9 + (−7𝑥)
3
7
9. 2 + 5 + (− 2) + 11
11. −𝑥 + [−𝑦 + (𝑥 − 𝑦)]
Section 2.3: Rules for Addition
Evaluate each expression if x = -3, y = 6, and z = -4.
12. −21 + 𝑥 + 𝑧
13. 1 + (−𝑦) + 𝑧
14. |𝑥 + (−𝑦) + 𝑧|
Simplify.
15. −(−𝑥 + 𝑦) + 𝑦
16. 𝑥 + [−(𝑥 + 𝑦)]
17. −(𝑥 + 4𝑦 + 3𝑥)
Section 2.4: Subtracting Real Numbers
Simplify.
18. (40 − 50) − (73 − 60)
20. −(4 − 𝑥)
19. −6 − 19 + 4 − 8 + 20
21. 8 − (𝑥 + 8)
22. 𝑥 + 8 − (−9 + 𝑥)
23. Becky took the subway from a stop 52 blocks east of Penn Station to a stop 39 blocks west of Penn
Station. How many blocks did she ride?
Section 2.5: The Distributive Property
Simplify.
24. 6(50 − 3)
25. −4(𝑥 − 2)
26. (2𝑥 + 3𝑦)(−3)
27. 7 + 2(5 − 𝑥)
28. −2(2𝑥 − 6𝑥𝑦 − 3𝑦)
29. 6(𝑥 + 2) − 4(−2𝑥 − 1)
31. (−7𝑎)(−5𝑐)2
32. −[(−2)(𝑥 + 𝑦)]
Section 2.6: Rules for Multiplication
Simplify.
30. 54(0)(−2)(31)
33. −3(7𝑥 + 𝑦) − 2(10𝑦 − 𝑥)
34. −15 + (−3)[2(𝑥 − 2) − 2(1 − 𝑥)]
Section 2.7: Problem Solving Consecutive Integers
Define the variable, write an equation, solve, and answer the question.
35. The sum of three consecutive integers is 192. Write an equation if x is least of the three integers.
Then find the integers.
36. The sum of two consecutive odd integers is -44. Write an equation if x is the smaller of the two
integers. Then find the integers.
37. The larger of two consecutive even integers is six less than twice the smaller. Find the integers.
38. The smaller of two consecutive even integers is five more than one half of the larger. Find the
integer.
Section 2.8: The Reciprocal of a Real Number
Simplify.
1
39. 9𝑥𝑦 (− 3)
1
1
40. 5 (−45𝑥 + 10𝑦)
1
41.−3 [4 (12𝑥 + 1) − 4] + 10𝑥
Section 2.9: Dividing Real Numbers
Simplify.
𝑥
42. 4 ∙ 4
43.
−𝑦
,𝑦≠0
𝑦
44.
108𝑥
−9
45.
−3(−1)(6)
−3+2