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Solving by Combining Like Terms
Solving by Using the Distributive Property
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Equation Grab Bag
Word Problems
100
5h + 2 + 2h = 23
h = 3
100
2(x + 5) = 14
x = 2
100
Simplify. 8b + 3b
11b
100
4x + 9 = 33
x = 6
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
3b + b - 8 = 4
b = 3
200
5(d - 2) = 40
d = 10
200
Simplify. 19x - 24x
-5x
200
x + 3x = -8
x = -2
200

Mr. Cushman bought 7 Hannah Montana t-shirts for a total of $70. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Cushman buy?

n - # of t-shirts 7n = 70n. Each t-shirt cost $10.

300
3a + 12 - 6a = -9
a = 7
300
7(4 - t) = -84
t = 16
300
Simplify. 3 + 5(a + 4)
5a + 23
300
4(y - 2) + y = -13
y = -1
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
-6 = -3y + 4 + 5y
y = -5
400
-2(x - 9) = -24
x = 21
400

Simplify. - (2b - 4)

-2b + 4

400
-6(m + 1) + 18 = 24
m = -2
400

Mr. Bucci goes to the grocery store and purchases 17 bags of raisins. His total cost was $51. What was the cost for a bag of raisins?

r - cost of a bag of raisins 17r= 51 r = 3 Each bag of raisins cost $3.

500
78 = 3c + 12 - c + 4
c = 31
500
-13(4 + 2a) = 208
a = -10
500

Simplify. 7(t + 8) - 5t + 4

2t + 60

500
7k - 8 + 2(k + 12) = 52
k = 4
500

When you count by ones from any 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.