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Grade 7 Unit 6 Expressions, Equations, & Inequalities

Total questions: 80

Worksheet time: 3hrs 31mins

Name
Class
Date
1.

Choose the equivalent expression.

15 + 4(5y + 10)

a)

5y + 25

b)

20y - 25

c)

20y + 40

d)

20y + 55

2.
Which expression is equivalent to 6(3y - 2y + 7)?
a)
18y + 7
b)
21y - 14y + 7
c)
18y + 42
d)
6y + 42
3.

Which of the following is NOT equivalent to 42x + 24?

a)

2(21x + 12)

b)

3(14x + 8)

c)

6(7x + 4)

d)

7(6x + 17)

4.
x - 8 = -5 
a)
13
b)
-13
c)
3
d)
-3
5.

Factor 12x - 20

a)

6(2x - 3)

b)

4(3x - 5)

c)

4x(3x - 5)

d)

3(4x + 6)

6.
Factor:  
4x + 30y
a)
2(x + 15y)
b)
4(x + 15y)
c)
2(2x + 15y)
d)
can't be factored
7.

WRITE AN EQUATION

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

a)

7x+6=331

b)

13x=331

c)

6x+7=331

d)

331-7=6x

8.

WRITE AN EQUATION

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

a)

24-10=7x

b)

7x- 24=10

c)

7x+ 10=24

d)

10+x=14

9.
Jared made sixty dollars mowing lawns over the summer. If he spent thirty-nine dollars buying new mower blades, how many seven dollar games could he buy with the money he had left?
a)
21 games
b)
3 games
c)
7 games
d)
99 games
10.
A bag of candy was shared equally among 4 friends.  Each friend gave away 7 pieces of candy.  They each ended up with 8 pieces of candy.  Write an equation to find how much candy was in the bag at the beginning.
a)
c/7 - 4 = 8
b)
c/4 + 7 = 8
c)
4/c - 7 = 8
d)
c/4 - 7 = 8
11.
Write the inequality for the following graph:  
a)
x ≥ 4
b)
x ≤ 4
c)
x > 4
d)
x < 4
12.
10 < 3x + 19
a)
x < 3
b)
x > 3
c)
x < -3
d)
x > -3
13.
Solve the inequality:  -3x + 4 > -2
a)
x < -1
b)
x > -1
c)
x < 2
d)
x > 2
14.
Pheobe has $500 in a savings account at the beginning of the summer. She wants to have at least $200 in account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Write an inequality that represents Pheobe's situation.
a)
200+25w ≥ 500
b)
500-25w ≥ 200
c)
500+25w ≤ 200
d)
200-25w ≤ 500
15.
Solve the inequality.
x + 5 ≤ 13
a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8 
d)
x ≤ 18 
16.
Match the graph with its inequality.
a)
11 < a
b)
11 > a
c)
 11 ≤ a
d)
 11 ≥ a
17.
x/5 = 6
a)
x = 5
b)
x = 6
c)
x = 10
d)
x = 30
18.
Steven has 5 more x-box games than Devin.  Devin's number of x-box games can be represented by n.  Which expression can show the number of games Steven has?
a)
n + 5
b)
5n
c)
5 - n
d)
n - 5
19.
Shelby has 4 more than twice as many trophies as Jon.  If Jon has x trophies, how many more does Shelby have?
a)
4x
b)
4 + 2
c)
4 + 2x
d)
4 + x
20.
An inverse operation is
a)
reversing the sign in an inequality
b)
using the opposite operation to solve equations
c)
 A number’s distance from zero
21.
Like terms are 
a)
numbers or same variable raised to the same power
b)
equal numbers
c)
only unknown values
22.
One difference between equations and expressions would be...
a)
you solve both of them using inverse operations.
b)
you flip the symbol when you multiply or divide by a negative
c)
equations have an equals because they show two equal expressions. Expresions have terms and operations.
23.
When solving an inequality, what is the main things that are different from solving equations.
a)
Draw the line
b)
Use inverse operations to solve.
c)
Bring down the inequality symbol and FLIP the symbol  when you multiply or divide by a negative.
24.
Choose an expression that is equivalent to the following
6n + 2(3 - 5n)
a)
n + 6
b)
6 - 4n
c)
16n + 6
25.
Choose the first step in solving the following equation.
-3y - 12 = 14
a)
add 3 from both sides
b)
add 12 to both sides
c)
subtract 12 from both sides
26.
What does this symbol mean?
a)
at least
b)
at most
c)
less than
27.
-12x > 36
a)
x > -3
b)
x > 48
c)
x < -3
28.
Simplify - ( - 12y + 8)
a)
12y + 8
b)
12y - 8
c)
-12y - 8
29.
- 3( 4 - 2x) = 6
a)
x = 1
b)
x = -3 
c)
x = 3
30.

Which number line shows all the values of x that makes the inequality true?

a)

a

b)

b

c)

c

d)

d

31.

Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29.

Which of these inequalities describes this situation, where n

is the number of songs Lin wants to buy?

a)

9.99+1.29n≥50

b)

9.99+1.29n≤50

c)

9.99−1.29n≥50

d)

9.99−1.29n≤50

32.

Select all expressions that are equivalent to 6x+1−(3x−1)

a)

6x+1−3x−1

b)

6x+-3x+1+1

c)

3x+2

d)

6x−3x+1−1

e)

6x+1+-3x−-1

33.

The answer to this inequality 5 − 2t < -4 is t > 9/2

Why does the inequality change from the less than symbol to the greater than symbol.

a)

I will divide by a negative 2.

b)

I will multiply by a negative 2.

c)

I will add negative 2.

d)

I don't know; I am negative.

34.
-6k + 7k=
a)
k
b)
-k
c)
12k
d)
-12k
35.
n -10 +9n -3=
a)
-3
b)
9n-3
c)
n
d)
10n -13
36.
Simplify the following expression:
19 - ( 3 - 5b)
a)
16 + 5b
b)
21 + 5b
c)
16 - 5b
d)
21 - 5b
37.
Simplify: -2(y - 4) + 5y
a)
-7y + 8
b)
3y + 8
c)
3y - 8
d)
-7y - 8
38.
Factor: 5x - 35
a)
5(x + 7)
b)
(x - 7)
c)
5(x - 7)
d)
(x + 7)
39.
Simplify the expression:
6 + 2(7x - 3) 
a)
12 + 7x
b)
14x
c)
14x + 3
d)
9 + 7x
40.

If y=10,find the value of 3+y =

a)

13

b)

-13

41.
6 - 3a = 21
a)
a= 9
b)
a= -9
c)
a= -5
d)
a= 5
42.
Solve for t.

6t + 4 ≤ -2
a)
t ≤ -1 
b)
t ≤ 1
c)
t=1
d)
1=t
43.
Jared made sixty dollars mowing lawns over the summer. If he spent thirty-nine dollars buying new mower blades, how many seven dollar games could he buy with the money he had left?
a)
21 games
b)
3 games
c)
7 games
d)
99 games
44.

Which of the following is equivalent to the expression shown?(7.EE.A.1)

2(1 − x) + 3x

a)

2 + x

b)

2 + 2x

c)

2 + 4x

d)

2 + 5x

45.

Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, x, plus a $10 fee. Amanda paid less than $27. Which inequality represents this situation and what quantities are true for x?

a)

2x+10≥27, where x≥8.5

b)

2x+10<27, where x<8.5

c)

2x+10≤27, where x≤8.5

d)

2x+10>27, where x>8.5

46.
Simplify by combining like terms:
5a + 2b - 3a + 4
a)
8a + 2b + 4
b)
2a + 2b + 4
c)
8ab
d)
4ab + 4
47.
Simplify the expression:
8(5 + w)
a)
40 + w
b)
40+8w
c)
85 + 8w
d)
13+8w
48.
(7a + 4) - (9a + 2)
a)
-2a + 6
b)
2a + 6
c)
-2a + 2
d)
2a + 2
49.

Select all the equations where x=3 is a solution. (3 total)

a)

x - 3 = 0

b)

1 + x = 2

c)

9 - x = 3

d)

6 = 2x

e)

x2 = 9

50.

Which expression is equivalent to 20c - 8d

a)

2(10c + 4d)

b)

4(5c - 8d)

c)

4(5c - 2d)

d)

c(20 - 8d)

51.

A symbol, often a letter, representing a quantity in an expression or mathematical equation.

a)

reciprocal

b)

expression

c)

variable

d)

coefficient

52.
Which equation describes the table? 
a)
y = 1/4x 
b)
y = 4 - x 
c)
y = 4 + x 
d)
y = 4x 
53.
What is the missing value in the table? 
a)
11
b)
24
c)
8
d)
9
54.
What is the missing value? 
a)
12
b)
20
c)
26
d)
16
55.
Which equation matches the table?
a)
c = 2h
b)
c = 6h
c)
c = 10h
d)
c = 12h
56.
Which equation describes the table shown:
a)
y = 1x + 2
b)
y = 1x - 2
c)
y = 2x + 1
d)
y = -2x + 2
57.
Peter had $50. Every week he babysits he gets $20.
Which equation describes the relationship between Peter's total money (s) and the number of weeks he babysits (w)
a)
s=50+200w
b)
s=200+50w
c)
s=20+50w
d)
s=50+20w
58.
Erin can read at least 80 words per minute. Write an inequality to show this situation. 
a)
x > 80
b)
x < 80
c)
x ≥ 80
d)
x ≤ 80
59.
Lindsay had $40. She works at the grocery store and earns $15 each day.
Which equation shows the relationship between Lindsay's savings (y) and the number of days Lindsay works (x)
a)
y = 15x + 40
b)
x = 15y + 40
c)
y = 40x + 15
d)
y = 40 - 15x
60.
Solve the inequality.
x + 5 ≤ 13
a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8 
d)
x ≤ 18 
61.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥ 
c)
<,≥
d)
≤,>
62.
When you graph an inequality, you used a closed dot when you use which symbols?
a)
≤, ≥ 
b)
<, >
63.
b > 32
Which value for "b" would make the inequality true?
a)
61
b)
32
c)
19
d)
27
64.
You spent less than 5 hours on homework each night.
a)
x > 5
b)
x < 5
c)
x ≤ 5
d)
x ≥ 5
65.
What inequality does the number line represent?
a)
x ≥ 3
b)
x > 3
c)
x < -3
d)
x ≤ -3
66.
What inequality does the number line represent?
a)
x ≤ 4
b)
x ≥ -4
c)
x < -4
d)
x < 4
67.
Today's temperature will be at least -4 degrees.
a)
t < -4
b)
t > -4
c)
t ≤ -4
d)
t ≥ -4
68.
a)
A
b)
B
c)
C
d)
D
69.
a)
18
b)
-18
c)
16
d)
72
70.
a)
-28
b)
-108
c)
28
d)
108
71.
4x = 16
a)
Expression
b)
Equation
c)
Inequality
72.
2p + 12 > 30
a)
Expression
b)
Equation
c)
Inequality
73.
6m + 13 - 5y
a)
Expression
b)
Equation
c)
Inequality
74.
Simplify by combining like terms:
5a + 2b - 3a + 4
a)
8a + 2b + 4
b)
2a + 2b + 4
c)
8ab
d)
4ab + 4
75.
3x-5x
a)
2x
b)
8x
c)
-2x
d)
15x2
76.
Simplify the expression:
n -10 +9n -3
a)
-3
b)
9n-3
c)
n
d)
10n -13
77.
Which of these are like terms in the following expression:
3x + 7 - 9x + 24y + 2x2
a)
7, 24y
b)
3x, 9x
c)
3x, -9x
d)
3x, -9x, 2x2
78.
Simplify the expression: 7v + 2 + 12 + 2v
a)
23
b)
23v
c)
9 + 14v
d)
9v + 14
79.
a + a + a + a
a)
a + 4 
b)
4a 
c)
a to the fourth power 
d)
4a + 4 
80.
y + x + y + y + x 
a)
2 + 3 
b)
x + y 
c)
2x + 3y 
d)
5xy 

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