Solving by Combining Like Terms
Solving by Using the Distributive Property
Expressions
Equation Grab Bag
Word Problems
Definitions
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.
100
What is a coefficient?
The number that is multiplied by the variable or symbol. The number that comes before the variable.
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 $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
200
What does it mean to distribute? Write in words how you would simplify the following:
- (x - 3)
In math, "to distribute" means to use the distributive property, which involves multiplying a number outside of parentheses by each term inside the parentheses. If a negative is outside the parenthesis we treat the "-" as "-1". In this case, we multiply -1 by x and multiply -1 by -3. And add the terms together.
Simplified: -x +3
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.
300
What are inverse operations?
In math, "inverse operations" are pairs of operations that "undo" each other, meaning if you perform one operation followed by its inverse, you will end up with the original value; for example, addition and subtraction are inverse operations, as are multiplication and division.
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 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
400
What is the definition of a constant? For the following, determine all the terms that represent constants and write them down.
3x + 4 -9x -8 = 23 + 7x
Constant: a fixed value.
4, -8, 23
500
78 = 3c + 12 - c + 4
c = 31
500
-13(4 + 2a) = 208
a = -10
500
Simplify.
7(t + 8.5) - 5t + 4
2t + 63.5
500
7k - 8 + 2(k + 12) = 52
k = 4
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.
500
What is the definition of a term?
How many terms does the following equation have?
5x2 + 6x - 8 = 9x2 -7 + 4x
In math, a "term" refers to a single part of an expression, usually separated by addition (+) or subtraction (-) signs; it can be a number, a variable, or a combination of both multiplied together, representing a single mathematical unit within a larger expression.
Answer: 6 terms