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Worksheets

Expressions, Equations, Inequalities

Total questions: 60

Worksheet time: 2hrs 7mins

Name
Class
Date
1.
2r + 2 + 5r - 2 + r 
a)
8r 
b)
8r - 4 
c)
12r 
d)
7r + 4 + r 
2.
6x + 1 + 7x 
a)
13x - 1
b)
14x 
c)
7x + 6x + 1 
d)
13x + 1 
3.
3 + 5x + 4
a)
5x ∙ 7 
b)
12x 
c)
35x 
d)
5x + 7 
4.
5x + 3y + 5 + 4x + 3y + y + 8
a)
9x + 7y + 13
b)
6x + 2y + 2
c)
25x + 2y + 3
d)
x + 7y + 12
5.
-4(-4d - 5)
a)
-16d+20
b)
16+20
c)
16d+20
d)
16s-20
6.
-8(6x + 3) 
a)
48X+3
b)
-48X-3
c)
14x+3
d)
-48x-24
7.

-3(3 - 8j)

a)

-6 - 11j

b)

-9 - 8jj

c)

-9 + 24j

d)

9 - 24j

8.

-(6 - 4p)

a)

6 - 4p

b)

6 + 4p

c)

-6 + 4p

d)

6p - 4

9.
Simplify the following expression:
-9(14p - 8) - 4p
a)
130p - 72
b)
122p - 72
c)
-130p - 18
d)
-130p + 72
10.
Simplify the following expression:
x + 4 - 7(x - 5)
a)
-33x + 19
b)
-47x2 +  21
c)
33x - 19
d)
-6x + 39
11.

Simplify the following expression:

-8(5b + 2) - 7(b - 5)

a)

-33b + 19

b)

-47b - 21

c)

33b - 19

d)

-47b + 19

12.
Simplify
-2x - 4(4x - 8)
a)
-16x - 2
b)
-18x + 32
c)
18x - 32
d)
-16x + 2
13.

Factor 12x - 20

a)

6(2x - 3)

b)

4(3x - 5)

c)

4x(3x - 5)

d)

3(4x + 6)

14.

Factor completely: 6x + -3

a)

3(2x + -1)

b)

-2 + -1 + 6 + x

c)

6( -2 + x )

d)

3 ( 1 + 2x)

15.
Factor:
12x + 9
a)
3(4x + 3)
b)
x(12+9)
c)
3(4x - 3)
d)
not factorable
16.

Pick the correct inequality for the graph.

a)

A

b)

B

c)

C

d)

D

17.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

18.
4x - 2 ≤ -22
a)
x ≥ -5
b)
x ≥ -6
c)
x ≤ -6
d)
x ≤ -5
19.
7b - 3 < 11
a)
b < 2
b)
84 > b
c)
b > 2
d)
b < 84
20.

6 - 2h > 30

a)

h < 12

b)

18 > h

c)

h > -12

d)

h < -12

21.
-4x + 14 ≤ 54
a)
x ≥ - 10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
22.
When graphing b ≤ 6 would you use an open or closed circle?
a)
Open
b)
closed
23.
You can spend no more than 20 dollars on your mom's birthday present.
a)
x > 20
b)
x < 20
c)
x ≤ 20
d)
x ≥ 20
24.
you must be at least 48 inches to ride the roller coaster.
a)
x > 48
b)
x < 48
c)
x ≤ 48
d)
x ≥ 48
25.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

26.

Which graph matches the inequality

2 > p?

a)

A

b)

B

c)

C

d)

D

27.

Which graph matches the inequality

-2 ≥ n?

a)

A

b)

B

c)

C

d)

D

28.

Which graph matches the inequality

r ≥ -6?

a)

A

b)

B

c)

C

d)

D

29.

What inequality does the number line graph represent?

a)

x ≤ -4

b)

x ≥ -4

c)

x < -4

d)

x < 4

30.

Which of the following are like terms?

a)

3x, 5

b)

3x, 5x

c)

3x, 5y

d)

3, 5x

31.
The steps in solving 5b - 6 = 24 are: 
a)
Add 6 to both sides and divide both sides by 5
b)
Add 6 to both sides and multiply both sides by 5
c)
Subtract 6 from both sides then multiply both sides by 5
d)
Subtract 6 from both sides then divide both sides by 5
32.

Solve -5t + 9 = 24

a)

-3

b)

3

c)

12

d)

-6.6

33.

What is the most efficient first step to solve this equation:

11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

34.

Evaluate the following expression

5 (3x - 4) when x = 10

a)

130

b)

30

c)

170

d)

1530

35.
Which of the following is equivalent to 5(2x + 6)?
a)
10x + 30
b)
10x + 6
c)
40x
d)
2x + 30
36.
What was done to solve the equation?
(Line 1)          5x - 8 = 32
(Line 2)          5x = 40
(Line 3)          x = 8
a)
add 8 to both sides, then divide both sides by 5
b)
add 8 to both sides, then divide both sides by 40
c)
subtract 8 from both sides, then divide by 5
d)
subtract 8 from both sides, then multiply by 5
37.

Where does a mistake first occur? What should have been done?

a)

Line 2 - You should subtract 4 from both sides.

b)

Line 5 - Calculation error

c)

Line 2 - You should divide by 3 first.

d)

Line 4 - You should divide by -3 on both sides.

38.

Where does a mistake first occur? What should have been done?

a)

Step 1 - You should add 4 to both sides first.

b)

Step 2 - You should have multiplied 2 on both sides.

c)

Step 2 - Calculation error

d)

There are no mistakes.

39.

A coefficient is __________.

a)

the variable

b)

a constant

c)

an exponent

d)

the number that is multiplied by the variable

40.
A constant term has ______.
a)
no exponents
b)
no variables
c)
no numbers
d)
no letters
41.
Which of these are like terms?
-3x + 4 - 8x + 2xy
a)
-3x and -8x
b)
-3x and 4
c)
-3x and -8x and 2xy
d)
-8x and 2xy
42.
What is the coefficient here?
17u + 8
a)
17
b)
8
c)
17u
d)
-8
43.
Simplify:
-3(x - 4) + 3(a - 6)
a)
-3x + 3a - 6
b)
-3x + 3a - 30
c)
-9ab - 6
d)
-9ab - 30
44.
Simplify:
5(-8n +5) -4n
a)
-44n + 25
b)
36n + 25 
c)
36n -25
d)
-44n + 5
45.
How many terms are in the expression?
-5x + 6r -5p +2
a)
1
b)
2
c)
3
d)
4
46.

What is the first inverse operation needed to solve for p?

765 = 5p - 254

a)

Subtracting 254 from both sides

b)

Adding 254 to both sides

c)

Multiplying both sides by 5

d)

Dividing both sides by 5

47.

3c + 5 = 23

what is the first step?

a)

Add 5 to both sides

b)

Divide both sides by 3

c)

Subtract 5 from both sides

d)

Subtract 3 from both sides

48.
What is the first step to solve this equation:
11 - 3x = 44
a)
Add 3 to both sides
b)
Subtract 11 from both sides
c)
Add 11 to both sides
d)
Divide 3 on both sides.
49.

15 = 7 - 5x

What is the first step to solve this?

a)

Add 5 to both sides

b)

Subtract 7 from both sides

c)

Add 7 to both sides

d)

Divide both sides by 5

50.

Step 1 for solving this equation is

-6(w + 1) = -11

a)

Expand, distribute the -6.

b)

Subtract 1 from both sides

c)

Add 6 to both sides

d)

Add 1 to both sides

51.

Is the solution below correct? If not, where was the first mistake made?

5 = 2d - 18

-2d = -2d

3d = -18

÷3 = ÷3

d = 6

a)

Yes

b)

No, they should have added 18 to both sides instead of subtracting 2d from both sides.

c)

No, they forgot that -18 divided by 3 is -6, not 6.

d)

No, they should have subtracted 2 from both sides, not 2d.

52.

3x - 7 = 32

What is the first step to solve this?

a)

Add 7 to both sides

b)

Subtract 7 from both sides

c)

Subtract 3 from both sides

d)

Divide both sides by 3

53.

The steps in solving 5b - 6 = 24 are:

a)

Add 6 to both sides then divide both sides by 5

b)

Add 6 to both sides then multiply both sides by 5

c)

Subtract 6 from both sides then multiply both sides by 5

d)

Subtract 6 from both sides then divide both sides by 5

54.
Combine like terms
3x + 2x + 3y - 7y
a)
5x + 10y
b)
5x + 4y
c)
5x - 4y
d)
5x -10y
55.
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation to find out how many hours, h, they rented the Boat if the total cost was $33.
a)

h = 2(33) + 15

b)
33 = 15h + 2
c)

h = 15(33) + 2

d)
33 = 2h + 15
56.
Pizzazz Publications is having some books printed. The printer charges $800 plus $5 per book. What equation could help me find how many books can be printed for $4,000?
a)
800 + 5x = 4000
b)
800x + 5 = 4000
c)
4000 + 5x= 800
d)
800 + 5 = 4000
57.

Expand -4(5x - 3)

a)

20x - 3

b)

20x - 12

c)

-20x - 12

d)

-20x + 12

58.

Level 3

Identify the steps to solve for b

a)

Add 6 to both sides and divide both sides by 5

b)

Add 6 to both sides and multiply both sides by 5

c)

Subtract 6 from both sides then multiply both sides by 5

d)

Subtract 6 from both sides then divide both sides by 5

59.

Did Sarah make an error? If so, which is the best description of her error?

a)

She didn't distribute (expand) correctly. The second step should read 3x - 12 = 24

b)

She didn't distribute (expand) correctly. The second step should read -3x - 12 = 24

c)

She didn't distribute (expand) correctly. The second step should read -3x + 12 = 24

d)

She didn't make an error.

60.
Find the Error
What error did the student make when solving the equation:
5x + 6 =  66
5x - 6 = 66 -6
5x = 60
5*5x= 60*5
x = 300
a)
The student subtracted 6 from both sides instead of adding
b)
Student multiplied by 5 instead of dividing by 5
c)
Student got the wrong answer when subtracting 66-6
d)
The student did not correctly eliminate the variable from one side of the equation