Name____________________________________ Date___________________ Period_______
Lessons 6.1 – 6.3
Lesson 6.1
Review
Evaluating Algebraic Expressions
Define a variable, write an algebraic expression, and then evaluate the expression for the given
values.
In 1963, the entrance fee for ages 12-17 years old to Disneyland was $1.20. You needed tickets
to ride the rides, and the rides were rated by tickets: A – E. Examples of the “A ticket” rides were
the Sleeping Beauty Castle or the Main Street cars & carriages. The “B ticket” rides included
Dumbo and the Mad Tea Party. The “C ticket” rides included Peter Pan and the Autopia. “D
tickets” were for rides like Storybook Land or the Jungle River Cruise. An example of the “E ticket”
ride is the Matterhorn Bobsleds. Books of various combinations of these tickets could be
purchased, or you could purchase one ticket at a time at booths in the park. One “E ticket” for 1217 years old was $.50.
Answer the questions using the 1963 prices given.
1. Let’s say you want to go into Disneyland and then only purchase E tickets (the roller coasters
and “big” rides).
Define a variable:___________________________________________________
Write an algebraic expression:_________________________________________
How much would you pay that day if you ride:
a. 5 “E ticket” rides?
b. 8 “E ticket” rides?
c. 12 “E ticket” rides?
2. Let’s say your younger sibling is only 7 years old. His/her entrance is only $.60, and he/she is
only going to ride the Fantasyland rides that are “C tickets” that day ($.30 each).
Define a variable:___________________________________________________
Write an algebraic expression:_________________________________________
How much would it cost for him/her that day if he/she rides:
a. 6 “C ticket” rides?
b. 9 “C ticket” rides?
c. 14 “C ticket” rides?
3. Your mom just had a baby, and isn’t going to take the baby on anything except maybe the cars
up and down Main Street and the other “easy” stuff. It’s $1.60 for her to get in, and $.10 each
for the “A ticket” rides.
Define a variable:___________________________________________________
Write an algebraic expression:_________________________________________
How much would it cost for her that day if she rides:
3 “A ticket” rides?
a.
b. 5 “A ticket” rides?
c. 8 “A ticket” rides?
Evaluate each algebraic expression for the values given.
4. 21 + (−5𝑔)
5. 4ℎ
6.
−2𝑏+10
2
a. for 𝑔 = 3
a. for ℎ = 5
b. for 𝑔 = 23
b. for ℎ = −2
b. for 𝑏 = −2
c. for 𝑔 = −2
c. for ℎ = −15
c. for 𝑏 = 4
a. for 𝑏 = 2
Complete each table.
7.
𝒂
𝟐𝒂 + 𝟏𝟓
8.
𝒄
−5
2
−3
−5
0
6
4
1
(𝒄𝟐 − 𝟏𝟐)
9.
𝒅
+ 𝟓𝒅
𝟐
𝒅
10.
𝒎
4
2
8
−5
−12
6
−1
1
Lesson 6.3
−(𝟑𝒎 − 𝟏𝟓)
Simplify by Combining Like Terms.
Simplify each expression by combining like terms. If the expression is already simplified, state how
you know.
11. 8 + 5ℎ + 2
12. 5𝑝 – 7𝑝 + 13
13. 5𝑐 + 2𝑧
14. 4𝑔 + 5 – 2ℎ + 7ℎ
15. – 9𝑔 + 4𝑔
16. – 𝑥𝑦 + 8𝑥𝑦
17. 𝑚 + 6𝑚 + 1
18. 5𝑣 + 𝑤 + 𝑣 – 4𝑤
19. 3𝑎 + 2𝑏 + 6𝑎
20. 12𝑥 2 + 5𝑥
21. 4𝑚2 – 7𝑚2 + 𝑚 – 12𝑚
22. 11𝑛2 – 15𝑛2 + 3𝑛
23. 2𝑥 – 3𝑦 + 5𝑥 + 11 + 𝑦 – 4
Lesson 6.2
24. 7𝑔 + 2 – 3ℎ – 4𝑔 + 8 + 7ℎ
Distributive Property
Use the Distributive Property to Simplify
25.
5(𝑥 + 1)
26.
3(𝑦 + 10)
27.
5(𝑛 – 3)
(𝑧 – 6)4
29.
31.
5𝑤(3𝑥 – 4𝑦)
32. 3(2𝑣 – 7𝑤)
33. (15𝑐 + 20)3𝑐
35. 2ℎ(5 + 3𝑔ℎ)
36. 3𝑝(5𝑝 + 2𝑝2 )
34. 5𝑚(𝑚 + 2𝑛)
5(𝑎 – 6)
30. 10(2𝑔 + 4ℎ)
28.
Simplify each expression using the Distributive Property and Combining Like Terms
37. 7(𝑤 + 3)
38. 5𝑥 + 2(𝑦 + 𝑥)
39. 4(𝑟 + 3𝑡) – 2𝑟
40. (𝑔 + 4)ℎ + 3ℎ
41. 3𝑣𝑤 + 5(𝑣𝑤 – 𝑣)
42. 2(𝑎2 + 4𝑎𝑏) – 𝑎𝑏
Lesson 6.3
Reverse Distribution – Factoring Algebraic Expressions
Rewrite each expression by factoring out the greatest common factor.
43. 16𝑚 + 24
44. 18𝑛 – 81
45. – 2𝑝 – 34
46. 30 – 6𝑧
47. 12𝑥 – 6
48. – 35𝑚2 + 14𝑚
49. 8ℎ – 20ℎ2
50. 18𝑔 + 18
51. 5𝑏 2 – 15𝑎𝑏
52. 24𝑚𝑛 + 30𝑚
53. 11𝑐 2 – 33𝑐𝑑 + 22𝑐
54. 5 – 55𝑎
55. 12𝑧 3 + 16𝑧 2 – 8𝑧
56. 6𝑝4 + 12𝑝3 – 3𝑝2
57. 10𝑤 5 + 15𝑤 3 – 5𝑤 2 + 20𝑤
Lesson 6.3
Evaluating Algebraic Expressions
Evaluate each expression for the given value. Choose whether or not to factor or combine like
terms before evaluating.
58. – 24𝑎 + 14; 𝑓𝑜𝑟 𝑎 =
1
59. 16 – 14𝑏;
3
1
60. 4𝑓 2 – 16𝑓; 𝑓𝑜𝑟 𝑓 = – 3 2
𝑓𝑜𝑟 𝑏 = 0.5
61. 18𝑔 + 27𝑔3 ; 𝑓𝑜𝑟 𝑔 =
62. (2ℎ – 5) + (4ℎ + 3); 𝑓𝑜𝑟 ℎ =
7
64. 18𝑚 – 36𝑚 + 4; 𝑓𝑜𝑟 𝑚 = − 9
1
2
2
3
63. (9 + 4𝑘) + (3 – 5𝑘); 𝑓𝑜𝑟 𝑘 = −2
65. 4.5𝑛 + 2 + (−8.5𝑛) + 1; 𝑓𝑜𝑟 𝑛 = 7
𝟏
Evaluate each algebraic expression for 𝒙 = 𝟑, – 𝟐, 𝟎. 𝟐𝟓, and 𝟐 𝟑
66. – 9𝑥
67. 12𝑥 + 10
68. 10 – 3𝑥