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Worksheets

Balancing and Solving Equations

Total questions: 82

Worksheet time: 7hrs 58mins

Name
Class
Date
1.

How do you balance the equation: 9x = 72

a)

multiply by 9 on both sides of the equation

b)

divide by 9 on both sides of the equation

c)

divide by 72 on both sides of the equation

d)

add 9 on both sides of the equation

2.

How do you balance the equation:

b - 16 = 53

a)

divide by 53 on both sides of the equation

b)

multiply by 16 on both sides of the equation

c)

subtract 16 on both sides of the equation

d)

add 16 on both sides of the equation

3.

How do you balance the equation:

g ÷ ⅝ = 1¾

a)

multiply by ⅝ on both sides of the equation

b)

divide by ⅝ on both sides of the equation

c)

add ⅝ on both sides of the equation

d)

multiply by 1¾ on both sides of the equation

4.

How do you balance the equation:

6.05 = t + 1.98

a)

add 1.98 on both sides of the equation

b)

subtract 1.98 on both sides of the equation

c)

add 6.05 on both sides of the equation

d)

subtract 6.05 on both sides of the equation

5.

Solve the equation: ⅙y = 2⅔

a)

y = 16

b)

y = 6

c)

y = ⅔

d)

y = 1½

6.

Solve the equation: h + 0.107 = 3.51

a)

h = 13.450

b)

h = 3.1

c)

h = 3.403

d)

h = 3.607

7.

4v = 7⅕

a)

v = 36

b)

v = 1⅗

c)

v = 9

d)

v = 1⅘

8.

solve the equation: x ÷ 2¼ = ½

a)

x = 2/9

b)

x = 5½

c)

x = 1

d)

x = 1⅛

9.

solve the equation: w - ⅜ = ⅙

a)

w = 7/16

b)

w = 9/10

c)

w = 13/24

d)

w = 24

10.

Balance the equation: 5⅓k = 8/9

a)

k = ⅓

b)

k = 6

c)

k = ⅙

d)

k = 15½

11.
To solve x - 4 = 7, what would you do to both sides?
a)
add 7 to both sides
b)
subtract 7 from both sides
c)
add 4 to both sides
d)
subtract 4 from both sides
12.
To solve 13 = x + 5, what do you do to both sides?
a)
Subtract 5 from both sides
b)
Add 5 to both sides
c)
Subtract 13 from both sides
d)
Add 13 to both sides
13.
To solve 15 = 9 + x, what do you do to both sides?
a)
Subtract 15 from both sides
b)
Add 15 to both sides
c)
Subtract 9 from both sides
d)
Add 9 to both sides
14.
To solve 4x = 20, what do you do to both sides?
a)
Subtract 4 from both sides
b)
Add 4 to both sides
c)
Multiply 4 on both sides
d)
Divide 4 from both sides
15.
To solve 15 = -3x, what do you do to both sides?
a)
Divide 3 from both sides
b)
Divide -3 from both sides
c)
Multiply by 3 on both sides
d)
Multiply by -3 on both sides
16.
To solve addition equations, you should...
a)
add
b)
subtract
c)
multiply
d)
divide
17.
To solve subtraction equations, you should...
a)
add
b)
subtract
c)
multiply
d)
divide
18.
To solve multiplication equations, you should...
a)
add
b)
subtract
c)
multiply
d)
divide
19.
To solve division equations, you should...
a)
add
b)
 subtract
c)
multiply
d)
divide
20.
To solve 10x = 45, what do you do to both sides?
a)
Subtract 10 from both sides
b)
Divide 10 from both sides
c)
Subtract 45 from both sides
d)
Divide 45 from both sides
21.
When solving equations, mathematicians want to get the variable (x) all by itself.
a)
True
b)
False
22.
If you subtract 2 from one side, you have to...
a)
add 2 to the other side
b)
subtract 2 from the other side
c)
multiply 2 on the other side
d)
divide 2 from the other side
23.
If you multiply one side by negative 11, you have to multiply the other side by negative 11.
a)
True
b)
False
24.
If you add -6 to one side, what do you do to the other side?
a)
Subtract -6
b)
Subtract  6
c)
Add -6
d)
Subtract -6
25.
To solve 4x = 20, what do you do to both sides?
a)
Subtract 4 from both sides
b)
Add 4 to both sides
c)
Multiply 4 on both sides
d)
Divide 4 from both sides
26.

10 x 2 = _____ x 5

a)

10

b)

25

c)

2

d)

4

27.

_____ x 6 = 3 x 10

a)

30

b)

5

c)

6

d)

3

28.

2 x 10 = 4 x _____

a)

5

b)

10

c)

20

d)

4

29.

9 x 4 = _______ x 6

a)

36

b)

9

c)

4

d)

6

30.

8 x 5 = _____ x 4

a)

8

b)

5

c)

10

d)

40

31.

_____ x 4 = 8 x 2

a)

8

b)

16

c)

3

d)

4

32.

4 x 6 = _____ x 3

a)

4

b)

6

c)

8

d)

12

33.

5 x 4 = ____ x 2

a)

5

b)

10

c)

4

d)

12

34.

(6x2)+(3x3)= _+_

a)

5+16

b)

6+12

c)

19+4

d)

3+6

35.

225+25=5x_

a)

5

b)

25

c)

50

d)

30

36.

Which statement is true?

a)

2x3=3x4

b)

10x1=5x2

c)

9x0=3x3

d)

5x4=3x6

37.
Solve the equation: 
x + 7 = 12
a)
x = 5
b)
x = 19
c)
x = -5
d)
x = 84
38.
Solve the equation:
x - 4 = 6
a)
x = 10
b)
x = -10
c)
x = 2
d)
x = -2
39.
Solve the equation:
4p = 16
a)
p = 12
b)
p = -12
c)
p = -4
d)
p = 4
40.
Solve for x:
a)
x = 20
b)
x = 7
c)
x = 10
d)
x = 3
41.
r + 20 = 27
a)
r = 7
b)
r = 47
c)
r = 13
d)
r = 20
42.

S + 4 = 24

a)

S = 28

b)

S = 6

c)

S = 18

d)

S = 20

43.

Solve the equation:

2p = 16

a)

p = 32

b)

p = 12

c)

p = 18

d)

p = 8

44.

x5=20\frac{x}{5}=20  

a)

100

b)

120

c)

4

d)

5

45.

4x = 8

a)

12

b)

2

c)

4

d)

3

46.
y - 4.6 = 12
a)
16.6
b)
5.8
c)
7.4
d)
Answer not Given
47.
Which equation has x = 5 as the solution?
a)
x + 15 = 10
b)
2x = 5
c)
2x = 10
48.
What equation matches this situation?
Robyn had some video games then bought 4 more.  Now she has a total of 10 games.
a)
v - 4 = 10
b)
v + 4 = 10
c)
10 - 4 = v
d)
Answer not Given
49.
2. Cheryl gets paid $8 per hour for her job at the record store.  She made a total of $96 last week.  Which equation models this situation?
a)
96h = 8
b)
h/96 = 8
c)
8h = 96
d)
h/8 = 96
50.
Martha baked cupcakes for 3 different classes. If each class needs 24 cupcakes which equation could be used to find x, the total number of cupcakes Martha will bake?
a)
3x=24
b)
x/3=24
c)
24x =3
d)
x/24 =3
51.

Which choice models this situation? Marcus needs to sell 25 tickets to a fundraiser by Friday. So far, he has sold 9 tickets. How many tickets does he still need to sell?

a)

t - 9 = 25

b)

t + 9 = 25

c)

9t = 25

d)

t/9 = 25

52.

Which choice models this situation?


Jack needed new pencils for school today. He took 6 pencils from a new box of pencils. If there are 18 pencils left in the box, how many pencils were in the brand new box?

a)

p - 6 = 18

b)

p + 6 = 18

c)

6p = 18

d)

p/6 = 18

53.

Becky is preparing for her younger sister's birthday party. She splits a jar of lollilops evenly among 6 goody bags. Each bag ends up with 4 lollipops.


Which equation can you use to find the number of lollipops n in the jar?

a)

n/6 = 4

b)

n - 4 = 6

c)

4n = 6

d)

n + 6 = 4

54.

Which choice models this situation?


Anna participated in a read-a-thon. Mr. Cole pledged $4 per book and gave Anna $44. How many books did Anna read?

a)

b - 4 = 44

b)

b + 4 = 33

c)

4b = 44

d)

b/4 = 44

55.
Solve the equation. Check your solution.
a)
72
b)
.5
c)
1/2
d)
2
56.
Solve the equation. Check your solution.
a)
80
b)
45
c)
180
d)
5
57.
What is the first step in solving the following equation?
3x - 5 = 20
a)
multiply both sides by 5
b)
add 5 to both sides
c)
divide both sides by 5
d)
subtract both sides by 5
58.
2 (n + 5) = -2 The first step in solving the following equation is ____________
a)
add five to both sides
b)
distribute 2 to all terms in the parenthesis
c)
add 2
59.
7(9 + K)= 84
k =____________
a)
3
b)
-3
c)
5
60.
m/9 - 1 = -2
a)
6
b)
9
c)
-9
61.
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.
62.
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
63.
Which equation would describe "two times a number plus five equals 15"?
a)
x + 5 = 15
b)
2x + 5=15
c)
x + 2(5) = 15
d)
2(x + 5) = 15
64.
Terry had his car repaired at Ace Auto.  He was charged $50 per hour of labor plus $150 for parts.  His total bill for the repair before tax was $375.  How many hours of labor was Terry charged for?
a)
2.5 hours
b)
4.5 hours
c)
7.5 hours
d)
10.5 hours
65.
Scott works on cars. He charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie's car bill was $63.
a)
7x + 35 = 63
b)
7x = 63
c)
7x - 35 = 63
d)
35x + 7 = 63
66.
Jim paid a gym membership fee of $50, plus $20 per month.  Jim has paid a total of $290 to the gym.  Which equation matches this situation?
a)
50 + 20m = 290
b)
20 + 50m = 290
c)
50 + 20 = m
d)
50m - 20 = 290
67.
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
68.
33 = 4a - 7
a)
a=-10
b)
a=10
c)
a=4.5
69.
6 - 3a = 21
a)
a= 9
b)
a= -9
c)
a= -5
d)
a= 5
70.
-3a + 8 = 14
a)
a= -2
b)
a= -7.5
c)
a= 2
d)
a= 6
71.
  x / 2  - 5 = 3
a)
x = -2
b)
x = 2
c)
x = 16
d)
x = 8
72.

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. What equation could be used to find out how many students were on each bus?

a)

331 = 7x + 6

b)

331 = 13x

c)

331 = 6x + 7

d)

331 - 7 = 6x

73.
Jim paid a gym membership fee of $50, plus $20 per month.  Jim has paid a total of $290 to the gym. How many months has he been a member at the gym?
a)
12
b)
17
c)
64.5
d)
15
74.

Scott works on cars. He charges $35 for each car plus $7 per hour. If Kylie's car bill was $63, how many hours did Scott work on her car?

a)

4 hours

b)

5 hours

c)

6 hours

d)

7 hours

75.
 A computer printer can print 10 pages per minute. There were already 35 pages in the tray.  The total pages printed was 115 pages. How many minutes has the printer been running?
a)
8
b)
9
c)
7
d)
10
76.
4 = 2(x + 3)
a)
1/2
b)
7/2
c)
-1
d)
5
77.

-5(2-w)=10

a)

3

b)

4

c)

10

d)

0

78.
a)
2
b)
4
c)
6
d)
8
79.
a)
60
b)
70
c)
80
d)
90
80.
a)

x = 40

b)

x = 400

c)

x = -40

d)

x = -400

81.

(a + 3)⁄7 = 3

a)

a= 18

b)

a= 21

c)

a= 4

d)

a= 11

82.
Solve for n:
3(n - 5) = -12
a)
1
b)
-1
c)
9
d)
-9

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