Equations with the Distributive Property

Question 1

Solve 6(n + 4) = 2(n + 18).

Accepted Answer

n = 3

Answer

n = -3/2

Answer

n = -3

Answer

n = 8

Question 2

A student solves 5(k + 12) = 75 by writing 5k + 12 = 75 and reaching k = 63/5. What went wrong?

Accepted Answer

the 5 had to multiply the 12 as well, so the left side is 5k + 60 and the solution is k = 3

Answer

nothing went wrong, and the solution really is k = 63/5

Answer

the 5 had to multiply the 12 but not the k, so the left side is k + 60 and the solution is k = 15

Answer

the 60 had to be added to the right side, so the solution is k = 27

Question 3

Solve 6(n - 3) = 2(n - 1).

Accepted Answer

n = 4

Answer

n = 17/4

Answer

n = -4

Answer

n = 1/4

Question 4

A student solves 8(b + 2) = 56 by writing 8b + 2 = 56 and reaching b = 27/4. What went wrong?

Accepted Answer

the 8 had to multiply the 2 as well, so the left side is 8b + 16 and the solution is b = 5

Answer

nothing went wrong, and the solution really is b = 27/4

Answer

the 8 had to multiply the 2 but not the b, so the left side is b + 16 and the solution is b = 40

Answer

the 16 had to be added to the right side, so the solution is b = 9

Question 5

A student solves 2(k + 7) = 36 by writing 2k + 7 = 36 and reaching k = 29/2. What went wrong?

Accepted Answer

the 2 had to multiply the 7 as well, so the left side is 2k + 14 and the solution is k = 11

Answer

nothing went wrong, and the solution really is k = 29/2

Answer

the 2 had to multiply the 7 but not the k, so the left side is k + 14 and the solution is k = 22

Answer

the 14 had to be added to the right side, so the solution is k = 25

Question 6

Solve -8(7w - 4) = 536.

Accepted Answer

w = -9

Answer

w = -71/7

Answer

w = 71/7

Answer

w = -8

Question 7

Solve -4(2b + 5) = -44.

Accepted Answer

b = 3

Answer

b = 49/8

Answer

b = 8

Answer

b = -8

Question 8

Solve -2(5n + 5) = 80.

Accepted Answer

n = -9

Answer

n = -15/2

Answer

n = -7

Answer

n = 7

Question 9

Solve 7(y + 7) = 2(y + 47).

Accepted Answer

y = 9

Answer

y = -2/5

Answer

y = -9

Answer

y = 87/5

Question 10

A student solves 7(k + 7) = 91 by writing 7k + 7 = 91 and reaching k = 12. What went wrong?

Accepted Answer

the 7 had to multiply the 7 as well, so the left side is 7k + 49 and the solution is k = 6

Answer

nothing went wrong, and the solution really is k = 12

Answer

the 7 had to multiply the 7 but not the k, so the left side is k + 49 and the solution is k = 42

Answer

the 49 had to be added to the right side, so the solution is k = 20

Question 11

Solve for b: 3(6b - 7) = 15.

Accepted Answer

b = 2

Answer

b = 11/9

Answer

b = -1/3

Answer

b = 12

Question 12

Solve 8(y - 4) = 4(y + 1).

Accepted Answer

y = 9

Answer

y = 33/4

Answer

y = -9

Answer

y = 2

Question 13

Solve for x: 6(4x - 12) = -192.

Accepted Answer

x = -5

Answer

x = -15/2

Answer

x = -11

Answer

x = -20

Question 14

A student solves 8(b + 4) = 56 by writing 8b + 4 = 56 and reaching b = 13/2. What went wrong?

Accepted Answer

the 8 had to multiply the 4 as well, so the left side is 8b + 32 and the solution is b = 3

Answer

nothing went wrong, and the solution really is b = 13/2

Answer

the 8 had to multiply the 4 but not the b, so the left side is b + 32 and the solution is b = 24

Answer

the 32 had to be added to the right side, so the solution is b = 11

Question 15

What value of n makes 4(6n + 7) = 268 a true statement?

Accepted Answer

n = 10

Answer

n = 87/8

Answer

n = 37/3

Answer

n = 11

Question 16

Solve 7(4x + 7) = -203.

Accepted Answer

x = -9

Answer

x = -15/2

Answer

x = -11/2

Answer

x = -36

Question 17

Solve 2(9a + 10) = -88.

Accepted Answer

a = -6

Answer

a = -49/9

Answer

a = -34/9

Answer

a = -5

Question 18

Solve -8(8b - 9) = 264.

Accepted Answer

b = -3

Answer

b = -21/4

Answer

b = 21/4

Answer

b = -2

Question 19

Solve for p: 5(7p + 4) = -50.

Accepted Answer

p = -2

Answer

p = -6/7

Answer

p = -14

Answer

p = -1

Question 20

Solve -8(3b - 8) = 112.

Accepted Answer

b = -2

Answer

b = -5

Answer

b = -22/3

Answer

b = 22/3

Question 21

What value of p makes 5(2p + 7) = -5 a true statement?

Accepted Answer

p = -4

Answer

p = -6/5

Answer

p = 3

Answer

p = -8

Question 22

What value of m makes 8(7m + 11) = -472 a true statement?

Accepted Answer

m = -10

Answer

m = -69/8

Answer

m = -48/7

Answer

m = -9

Question 23

Solve 7(n + 2) = 4(n + 5).

Accepted Answer

n = 2

Answer

n = -3

Answer

n = -2

Answer

n = 6

Question 24

Solve 9(y - 5) = 2(y + 9).

Accepted Answer

y = 9

Answer

y = 54/7

Answer

y = -9

Answer

y = 23/7

Question 25

What value of t makes 9(9t + 5) = 369 a true statement?

Accepted Answer

t = 4

Answer

t = 46/9

Answer

t = 5

Answer

t = 3

Question 26

Solve 6(x + 7) = 9(x + 2).

Accepted Answer

x = 8

Answer

x = 40/3

Answer

x = -8

Answer

x = -11/3

Question 27

Solve -6(7b + 4) = -192.

Accepted Answer

b = 4

Answer

b = 14/3

Answer

b = 36/7

Answer

b = -36/7

Question 28

Solve -5(6a - 6) = 150.

Accepted Answer

a = -4

Answer

a = -26/5

Answer

a = -6

Answer

a = 6

Question 29

Solve 6(9k + 3) = 504.

Accepted Answer

k = 9

Answer

k = 29/3

Answer

k = 10

Answer

k = 8

Question 30

Solve -8(5p + 6) = 312.

Accepted Answer

p = -9

Answer

p = -33/5

Answer

p = 33/5

Answer

p = -8

Question 31

Solve -7(5y + 4) = -203.

Accepted Answer

y = 5

Answer

y = 33/5

Answer

y = -33/5

Answer

y = 6

Question 32

What value of n makes 3(8n + 6) = -222 a true statement?

Accepted Answer

n = -10

Answer

n = -19/2

Answer

n = -17/2

Answer

n = -9

Question 33

Solve 4(n - 4) = 2(n - 3).

Accepted Answer

n = 5

Answer

n = 13/2

Answer

n = -5

Answer

n = -1

Question 34

Solve -6(6p + 5) = -174.

Accepted Answer

p = 4

Answer

p = 17/3

Answer

p = -17/3

Answer

p = 5

Question 35

Solve for n: 9(8n - 11) = 477.

Accepted Answer

n = 8

Answer

n = 61/9

Answer

n = 21/4

Answer

n = 9

Question 36

Solve for m: 2(6m - 5) = -70.

Accepted Answer

m = -5

Answer

m = -65/12

Answer

m = -20/3

Answer

m = -4

Question 37

Solve for w: 5(3w + 8) = 70.

Accepted Answer

w = 2

Answer

w = 22/3

Answer

w = 6

Answer

w = 3

Question 38

Solve 9(8b + 4) = -396.

Accepted Answer

b = -6

Answer

b = -50/9

Answer

b = -5

Answer

b = -7

Question 39

What value of x makes 9(6x + 2) = 558 a true statement?

Accepted Answer

x = 10

Answer

x = 32/3

Answer

x = 11

Answer

x = 9

Question 40

A student solves 7(b + 6) = 56 by writing 7b + 6 = 56 and reaching b = 50/7. What went wrong?

Accepted Answer

the 7 had to multiply the 6 as well, so the left side is 7b + 42 and the solution is b = 2

Answer

nothing went wrong, and the solution really is b = 50/7

Answer

the 7 had to multiply the 6 but not the b, so the left side is b + 42 and the solution is b = 14

Answer

the 42 had to be added to the right side, so the solution is b = 14

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Equations with the Distributive Property

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Glacier Rush

Board Games: Teacher-led, projected to the class

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Mystery Blast

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Castle Siege

Hot Potato

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King of the Hill

Bank Heist

Top Corner

Equations with the Distributive Property

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner