Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
Lesson 1: Commutative and Associative Properties
Homework
1) Identify the property as Commutative Property of Addition, Commutative Property of
Multiplication, Associative Property of Addition, or Associative Property of Multiplication
a. 4 + 7 = 7 + 4
b. 12 (10 x 8) = (10 x 12) 8
c. 5 x 4 = 4 x 5
d. (15 + 9) + 45 = 15 + (9 + 45)
e. 5(2x) = 2(5x)
f. 3 + (b + 9) = (3 + b) + 9
Lesson 2: Like Terms
Homework
2)
Create a like term for the given term.
a. 6x
b. Y
c. 10x2
d. 14xy
e. -5x
3)
Simplify the expression if possible.
a. 15x2 + 5x2 + 2x
b. -10y + 4y – 5
c. x + 2x + x + 5x
d. 6x2 + 5x2
e. 12x + 14x + 3y
f. 6y – 3y + 6xy + 4xy
g. 9y + 4y – 2y + y
h. x + 5x + x + 12 – 7x
i. 8x – 3x + 2x + 15 – 7x
Lesson 3: Distributive Property
Homework
4)
Use the Distributive Property to rewrite the expressions without parentheses
a. 5(x + 4)
b. 7(x – 12)
c. 3(x - 14)
d. -1(x – 2)
e. (x - 2)5
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
f. ⅔(6x + 12)
g. 2.5(3x – 4.1)
5)
Use the Distributive Property to factor the following expressions
a. 12b + 48
b. 6m + 14m
c. 16y + 56z
d. 8e + 24f + 28g
e. 12d2 + 15d
f. -14r + 21t
g. -9c – 15h
6)
If a triangle has a perimeter of 12w + 18, how much is each side?
Lesson 4: Simplifying Algebraic Expressions
Homework
7) Simplify the algebraic expression if possible.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
5x + 4x + 7y + 3y +12
22x + 9y – 14 x - 6y
25x – 15
2x + 42 x + 9x + 13
14x – 12x – 2x -9
23x + 28x + 11
5x + 7y + 4y + 16x
2(x+5) – 8 + 5x
6x + 5(x + 7)
3(4v + 10) + 8(5v + 2)
9 + 2k+ (7 – 2k)5
12j + 3(x + 6) + 19
12(x + 0.5) + 14(x + 2)
5(2t + 4) – (13t – 9)
Lesson 5: Inverse Operations
Homework
8)
Name the inverse operation needed to solve for the variable.
a. t – 18 = 54
b. 14x = 228
c. m + 19 = 51
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
d. 11b = 66
e.
m
2
4
Lesson 6: One Step Equations
Homework
9)
Solve.
a. n + 9 = 13
b. -14 + b = 21
c. z – 18 = -14
d. -7 + g = -12
e. 19 = 15 + y
f. b + (-4) = 13
g.
q
 33
3
h. -18x = -360
i. x – 11 = 4
j.
1
n  15
5
k. -15c = -75
l. -8 + r = 27
m. 19 + m = 3
n.
w
1
8
o. p – 4.8 = 11.2
𝑔
p.
= 2.2
3.4
q. 3.6m = 25.2
r.
s.
2
5
𝑡=
8
25
5
5
6
12
5 +𝑚 =3
Lesson 7: Two Step Equations
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
Homework
10) 2m – 8 = -28
x
38
11) 9
12) 12m + 20 = -40
x
 5  21
13) 3
14) 8r – 27 = -19
6
k
 33
3
15)
16) 15 = -4y – 9
17) 8w + 4 = -36
18) 4a – 15 = -23
19) 44 = 5x – 6
20) -3.7x + 5.6 = -5.87
21)
2
5
𝑥 + 7 = 8.32
𝑥
22) − + (−9.8) = −5.6
4
23) 3.7x – 2.2 = 16.3
24)
5
6
𝑥 − 3.7 = 11
17
20
Lesson 8: Multi-Step Equations
Homework
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
Solve.
25) 6(m + 4) – 2m = -8
26) 44 = 4(8 + h)
3
(8t  4)  2
27) 4
28) 3(5 – t) – 4t = 18
29) 2(y - 5) = 16
30) 0.1(h + 20) = 3
3z
45
8
31)
32) 8.6 = 6j + 4j
33) 12z – (4z + 6) = 82
34) 5.4d – 2.3d + 3(d – 4) = 16.67
3
1
3
p  4( p  12)  79.25
4
4
35)
36) -5.3m + (-3.9m) – 17 = -94.28
37) 6(3.5y + 4.2) – 2.75y = 134.7
Lesson 9: Distributing Fractions in Equations
Homework
38)
39)
40)
41)
42)
43)
44)
45)
2
9
5
(𝑥 + 4) = 6
(3𝑥 + 7) = 10
8
3
10
2
3
3
4
6
7
2
3
6
5
(𝑥 − 3) =
(𝑚 + 2) =
(2𝑥 + 7) =
6
10
4
5
9
4
(2𝑥 − 12) =
12
7
(6𝑥 + 18) = 20
(10𝑧 + 15) = −6
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
Lesson 10: Translating Between Words and Equations
Homework
46) Write an equation then solve.
a. You sell brownies for $3 each. You sold 12 more this week than last. Altogether,
you made $84. How many brownies did you sell each week?
b. Find the length of a rectangle if its width is 13 less than the length and its perimeter is
90 cm.
c. Six times the difference of a number and 9 is 19 less than the number.
d. Eight times seven more than a number is sixteen. What is the number?
Lesson 11: Using Numerical and Algebraic Expressions and Equations
Homework
47) Lucas, Jerrell, and Brianna all ran a marathon. Lucas ran 5/9 of the marathon, Jerrell ran
63% of the marathon, and Brianna ran 0.46 of the marathon. Who is in the lead?
48) Kiana bought a cardigan that originally cost $60. She had a 25% off coupon. How much
in total did Kiana pay?
49) Joel bought a laptop that cost $859.00. He had to pay 8% tax. How much in total did Joel
pay for his laptop?
50) Lorena had 2 times as many pencils as her brother. In total they have 27 pencils. How
many pencils does Lorena have? How many does her brother have?
51) Jose went to an all-you-can-eat buffet. He paid $15 for his meal and $2 for each soda. If
Jose spent $21, how many sodas did he buy?
Lesson 12: Inequalities with One Variable
Homework
52) Write an inequality for each sentence below, and then graph the solutions of each
inequality on a number line.
a. w is greater than 7.
b. p is less than or equal to -1.
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
c.
m is less than 5.
d. 11 is greater than or equal to k.
e. A number, f is positive.
f.
The total, t is fewer than 4 items.
g. 4 is less than a number, n.
h. The speed limit, s, cannot exceed 25 mph.
i.
A number c is at least 12.
j.
w is not more than 50.
k.
g is more than or equal to 8.
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
l.
h is not less than -5.
m. The time, t for lunch cannot exceed 30 minutes.
n. At most, 25 students, s, will be in the class.
o. To have an A in class, g, must exceed a 92.
53) Write an inequality for the graph below.
54) Write an inequality for the graph below.
55) Write an inequality for the graph below.
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
56) Write an inequality for the graph below.
57) Write an inequality for the graph below.
58) Write an inequality for the graph below.
59) Explain how you know if the endpoint of the graph in an inequality should be an open dot
or a closed dot.
Lesson 13: Simple Inequalities Involving Addition and Subtraction
Homework
60) Solve, check and graph the following inequalities.
a. x + 7 > -2
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
b.
c.
d.
e.
f.
g.
h.
i.
j.
x + 3 < -3
-8 < x + 15
x–4≤1
x–1>6
-7 + x ≥ -11
-6 ≤ x – 2
x + 2.5 < 6
-5.5 ≤ x – 3.25
7.9 > x + 4.4
61) Write an inequality for each sentence below and then solve and check it.
a. The difference of a number and seven is at most 16.
b. 18 is less than a number plus 7
c. h decreased by 3 is more than 1.
d. 14 is greater than or equal to the sum of 18 and a number.
e. The sum of b and 22 is at least 6
62) Suppose you must maintain at least $500 in your checking account in order to have free
checking. Your balance is $612 and then you make a deposit of $79. How much can you
withdraw and still keep your free checking? Write an inequality and solve.
63) You need no more than 2,200 calories in a day. You had 720 calories at breakfast and
plan on having 1,000 calories at dinner. How many calories, c can you eat for lunch?
Write an inequality and solve.
Lesson 14: Simple Inequalities Involving Multiplication and Division
Homework
64) Solve, check and graph the following inequalities.
a. 4x ≤ -16
b. 32 ≤ 8x
c. -7x > 49
d. -5x < -55
e. 13x ≥ 0
f. 60 < 12x
g. 66 > -3x
h. -6x ≥ 360
i. -2x ≥ 17
j. 26 < 4x
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
65) Solve, check and graph the following inequalities.
a. 5 ≤
b.
c.
d.
𝑥
3
−8
3
g.
h.
i.
j.
-4 ≥
𝑥
−4
𝑥
4
≥0
> 11
e. 4 ≤
f.
3
< -3
𝑥
𝑥
𝑥
𝑥
−1
𝑥
−6
≥ -1.5
≤ 12
𝑥
−6
𝑥
−2
> -9
< 3.3
66) Write an inequality for each sentence below and then solve and check it.
a. Four times a number n is no more than 24.
b. One-third of m is greater than 9.
c. The product of -9 and g is at most 81.
d. Half of d is less than or equal to 16.
e. The quotient of v divided by -6 is less than 4.
f. The product of 7 and x is no less than -42.
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Unit 2: Expressions & Equations Homework Problems
Do all assignments from this packet in your spiral notebook! Copy the
problems into your notebook, show work, and circle your answers!
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