Solving by Combining Like Terms

Solving by Using the Distributive Property

Expressions

Equation Grab Bag

Word Problems

5h + 2 + 2h = 23

h = 3

2(x + 5) = 14

x = 2

Simplify.
8b + 3b

11b

4x + 9 = 33

x = 6

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.

3b + b - 8 = 4

b = 3

5(d - 2) = 40

d = 10

Simplify.
19x - 24x

-5x

x + 3x = -8

x = -2

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

3a + 12 - 6a = -9

a = 7

7(4 - t) = -84

t = 16

Simplify.
3 + 5(a + 4)

5a + 23

4(y - 2) + y = -13

y = -1

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.

-6 = -3y + 4 + 5y

y = -5

-2(x - 9) = -24

x = 21

Simplify.
- (2b - 4)

-2b + 4

-6(m + 1) + 18 = 24

m = -2

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

78 = 3c + 12 - c + 4

c = 31

-13(4 + 2a) = 208

a = -10

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

2t + 63.5

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

k = 4

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.

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