Solving Equations with Distributing and Combining Like Terms

Rewriting Equation

100

Solve for y.

3y – 1.5x = 6

y = 2 - 0.5x

200

Solve for y.

4.5 x− 1.5y = 5.4

y = −3.6 + 3x

300

Solve for y.

3y + x = 9

y = 3 – (1/3)x

400

Solve for y.

2y+5x=6

3 - (5/2)x

500

Solve for y.

4.2x – 1.4y = 2.1

y=-1.5-3x

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 + 6 = 3(a - 7)

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+2 )= 32

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