Show:
Solving by Combining Like Terms
Solving by Using the Distributive Property
Variables on Both Sides of Equation
One, Many, or No Solutions
Word Problems
100
5h + 2 + 2h = 23
h = 3
100
2(x + 5) = 14
x = 2
100

7 – 3n = –2n

7

100

–8 – 6g = –7g

One solution (g = 8)

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

10 + 8p = –10 + 4p

–5

200

9 + n + 11 – 14n = 4 – 13n

No solution

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
3a + 12 - 6a = -9
a = 7
300
7(4 - t) = -84
t = 16
300

–2 + 8c = –8 + 9c

6

300

18 + 8n = –2(–4n – 9)

Infinitely many solutions

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

–10(u – 1) = –1 – 9u +7

4

400

–3(p – 18) = 4 – 3p

No Solution

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

20r = –5(13r – 17)

r = 1

500

–6(–3t – 9) = 3(16 + 5t)

One solution. (t = –2)

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.