Solving Multi-Step Equations

Solving Equations

100

5h + 2 + 2h = 23

h = 3

200

4-3x=2x-6

x=2

300

3a + 12 = -9 +6a

a = 7

400

2y - 6 = -3y + 4 + 5y

no solution

500

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

infinite solutions

Solving by Using the Distributive Property

100

2(x + 5) = 14

x = 2

200

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

x = 4/7 

300

-(x - 2) = 0

x = 2

400

x/4 + 7=3

x = -16

500

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

x = 1/2

Expressions

100

Simplify. 8b + 3b

11b

200

Simplify. 19x - 24x

-5x

300

Simplify. 3 + 5(a + 4)

5a + 23

400

Simplify. - (2b - 4)

-2b + 4

500

Simplify. 7(t + 8.5) - 5t + 4

2t + 63.5

Equation Grab Bag

100

4x + 9 = 33

x = 6

200

x + 3x = -8

x = -2

300

4(y - 2) + y = -13

y = -1

400

-6(m + 1) + 18 = 24

m = -2

500

7k - 8 + 2(k + 12) = 52

k = 4

Word Problems

100

WRITE AN EQUATION & 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 age n + 3 = 11 n = 8 Julie's sister is 8 years old.

200

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?

n - # of t-shirts 7n = 90.93 n = 12.99 Each t-shirt cost $12.99

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?

a - # of apples in each box 4a - 3 = 109 a = 28 There were 28 apples in each box.

400

Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?

r - cost of a bag of raisins 17r + 2.97 = 34.76 r = 1.87 Each bag of raisins cost $1.87

500

When you count by ones fron many integer, you are counting 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.