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

Equations with Variables Both Sides

100

5x = 2x + 21

x = 7

200

3x + 13 = 8x - 2

x = 3

300

5x + 9 - x = 7 - 2x

x = -1/3

400

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

x = 13

500

x - 2(6 - x) = 8x - (x + 6)

x = -3/2

Equation Grab Bag

100

4x + 9 = 33

x = 6

200

x + 3x = -8

x = -2

300

4(y - 2) = 5y + 8 - y

No Solution!

400

6(m+2) + 18 = 4m + 2(m+15)

Infinitely Many Solutions!

500

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

x = 24/5

Word Problems.Write an Equation and Solve!

100

Write an Equation and Solve. Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

n = Julie's sister's ag.  n + 3 = 11

n = 8.  Julie's sister is 8 years old.

200

Write an Equation and Solve.  A family bought 7 NB t-shirts for a total of $90.93. Each t-shirt cost the same amount. What is the cost of each t-shirt?

n = # of t-shirts.  7n = 90.93

n = 12.99.   Each t-shirt cost $12.99

300

Write an Equation and Solve.  Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 1 apple and gives 2 away, there are 109 apples remaining. How many apples were originally in each box ?

a = # of apples in each box 4a - 3 = 109

a = 28.  There were 28 apples in each box.

400

Write an Equation and Solve.  A square with side length of 3x has the same perimeter as an equilateral triangle with side length of 2x + 4.  What is the perimeter of each shape?

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

Each shape has a perimeter of 24 units

500

Write an Equation and Solve.  Integers that are one after another are called consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?

n + (n + 1) + (n + 2) = 48.  n = 15 

The integers are 15, 16, and 17.