Solving Multi-Step Equations

Solving by Combining Like Terms

100

5h + 2 + 2h = 23

h = 3

200

3b + b - 8 = 4

b = 3

300

3a + 12 - 6a = -9

a = 7

400

-6 = -3y + 4 + 5y

y = -5

500

78 = 3c + 12 - c + 4

c = 31

Solving by Using the Distributive Property

100

2(x + 5) = 14

x = 2

200

5(d - 2) = 40

d = 10

300

7(4 - t) = -84

t = 16

400

-2(x - 9) = -24

x = 21

500

-13(4 + 2a) = 208

a = -10

Solve variables on Both Sides

100

2x + 6 = x - 5

x = -11

200

6x - 10 = -60 + 6x

no solution

300

3x + 5 = 2x + 12

x = 7

400

4(3x-4) = 2(5x+2)

x= 10

500

2(4-3x)-10 = 2x-74

x = 9

Types of Solutions

100

How many solutions does the equation have: 4x + 9 = 33

one solution

200

How many solutions does the equation have:   4x - 6 = 4x + 6

no solution

300

How many solutions does the equation have:   

4(-3x - 6) = -2(6x + 12)

infinite solutions

400

Write an equation that has no solution.

TBD

500

Find the missing numbers so that the equation has infinite solutions:

3x + 14 - x = ?(x + ?)

2 and 7

Word Problems

100

Mr. Cushman bought 7 Hannah Montana t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Cushman buy?

$12.99

200

Maria is buying notebooks and pens for school. Each notebook costs $3, and each pen costs $2. She buys 4 notebooks and some pens, spending a total of $22. How many pens did Maria buy?

5 pens

300

Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

There were 28 apples in each box.

400

Jordan and Taylor are saving money to buy a video game console. Jordan saves $10 each week and already has $40. Taylor saves $8 each week and already has $60. After how many weeks will they have the same amount of money saved?

10 weeks

500

When you count by ones from many integer, you are counting consecutive integers. Using variables, three consecutive integers are x, x + 1, and x + 2. The sum of three consecutive integers is 48. What are the integers?

The integers are 15, 16, and 17.