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Solving Multi-Step Equations with Variables on Both Sides Lesson

Total questions: 20

Worksheet time: 1hrs 13mins

Name
Class
Date
1.
2x - 3 + 4x = 27
a)
12
b)
4
c)
5
d)
15
2.
3x - x + 4 = 4(2x +1)
a)
no solution
b)
all real numbers (infinite)
c)
x = 6
d)
x = 0
3.
2x + 3(5x - 7) = 47
a)
x = 1
b)
x = 2
c)
x = 3
d)
x = 4
4.
5x - 14 = 8x + 4
a)
6
b)
-6
c)
-18/13
d)
10/3
5.
38 + 7k = 8(k + 4)
a)
6
b)
8
c)
-6
d)
1
6.

Pristine House Cleaners charges $19.85 plus $32 per room. Sparkle House Cleaners charges $61.85 plus $18 per room. Write and solve an equation to find the number of rooms for which the total cost of both house cleaners is the same.

a)

4 rooms

b)

1/3 rooms

c)

3.5 rooms

d)

3 rooms

7.

Solve for v.

a)

60

b)

-3

c)

15

d)

3

8.

Solve for x.

a)

55

b)

60

c)

15

d)

35

9.

Solve the equation:

½ (2x + 6) = 3x + 13

a)

no solution

b)

x = 8

c)

x = -5

d)

x = 7

10.

½x + ⅓x = 5

a)

x = ⅕

b)

x = 1

c)

x = 5

d)

x = 6

11.

During the fall, you decide to rake leaves and charge $12 for coming to a house and raking, and then $9 for every hour you rake. If you make $57 in each of 3 houses you went to in one day, how many hours did you spend shoveling?

a)

2 hours

b)

12 hours

c)

15 hours

d)

10 hours

12.
A toy company spends $1500 per day for factory expenses plus $8 to make each teddy bear.  They sell the teddy bears for $12 a piece.  Which equation could be used to find the number of bears t the company has to sell in one day to equal its daily cost?
a)
1500 + 8t = 12
b)
12 + 8t = 1500
c)
1500 + 8t = 12t
d)
8t = 12t + 1500
13.
Jason says that 10 less than one third of his age is 11 years old.  How old is Jason?
a)
3 years old
b)
7 years old
c)
57 years old
d)
63 years old
14.
Maria has 25 dollars.  She has to buy a gallon of milk which costs $3.50.  She wants to spend the rest of her money on cereal.  If each box of cereal costs $4.50, how many can she purchase?
a)
4 boxes
b)
5 boxes
c)
6 boxes
d)
7 boxes
15.
WRITE AN EQUATION
Aliyah had some candy to give to her four children. She first took ten pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?
a)
(x-10)/4=2
b)
x-10/4=2
c)
x-10=2(4)
d)
2(x-10)=4
16.
After paying $3.32 for a sandwich, Brenda has $19.79. How much money did she start with? Which equation could you use to solve this problem?
a)
3.32m=19.79
b)
m-19.97=3.32
c)
m-3.32=19.79
17.

Garland put 2b + 3 dollars in the bank in the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week he doubled what was in the bank and put that amount in the bank. If he now has $477 in the bank, how much did he put in the bank the first week?

a)

$66

b)

$53

c)

$32

d)

$48

18.

Nendell saw the following sign at a diner. If he bought one of each item and spent $7.50, how much did the drink cost?

a)

$1.50

b)

$1.37

c)

$1.57

d)

$1.62

19.

Mel is 3 years older than Rahfat and Aurelio is twice as old as Mel. The sum of their ages is 57. How old is Mel?

a)

13

b)

21

c)

18

d)

15

20.
Joe's BBQ sells BBQ by the pound.  Michelle buys $8.75 worth of sides and then 6 pounds of barbeque.  If her total bill was $40.55, how much was each pound of barbeque?
a)
$5.30
b)
$3.95
c)
$8.22
d)
$5.32