Solving Equations with Distributing and Combining Like Terms

Surprise!

100

Solve for b:

A = bh

b = A/h

200

A certain amount of nickels and dimes total 80 cents. 

What is one possible solution for the amount of nickels and dimes?

1 dime, 14 nickels

2 dimes, 12 nickels

3 dimes, 10 nickels

4 dimes, 8 nickels

etc.

300

Solve for y.

8x + 2y = 20

y = 10 - 4x

400

Solve for y.

3x + 4y = 48

y = 12 - 3/4x

500

Find the y values for the given x-values for the equation 3x + 4y = 48.

x = 4

x = 8

x = 2, y = 9

x = 8, y = 6

Equations with Variables on Both Sides

100

Solve for the variable:

5x = 3x + 20

x = 10

200

Solve for the variable:

6m - 7 = 2m + 25

m = 8

300

Solve for the variable:

10k + 30 = -2k + 54

k = 2

400

Solve for the variable:

-6a + 5 = 3a - 22

a = 3

500

Solve for the variable:

-p + 31 = 5p + 1

p = 5

Two-Step Equations

100

Solve for the variable:

2x + 1 = 7

x = 3

200

Solve for the variable:

x/7 - 2 = 4

x = 42

300

Solve for the variable:

8a - 3 = 61

a = 8

400

Solve for the variable:

-9m + 2 = 83

m = -9

500

Solve for the variable:

g/10 + 5 = -1

g = -60

Combining Like Terms

100

Combine like terms:  

2a + 3a + 5a

10a

200

Combine like terms:  

7b+ 11 + 2b

9b + 11

300

Combine like terms:  

5a + 9a - 3a + 2a

13a

400

Solve for the variable:

7m + 3m = 70

m = 7

500

Solve for the variable:

3a - a + 4a = 30

a = 5

Distributive Property

100

Simplify:

3(a + 2) 

3a + 6

200

Simplify:

7(5k - 8)

35k - 56

300

Simplify:

-9(3a - 5)

-27a + 45

400

Solve for the variable:

4(2a + 1) = 20

a = 2

500

Solve for the variable:

5(3y - 2) = 50

y = 4