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9 week exam - Expression & Equations Study Guide
Solve these problems to see what the questions on the 9 week exam will be like! The answer key for the study guide
is posted on my web page under the Resources section!
Vocabulary
Label each part of the expression below using the following words: term, coefficient, constant, variable, expression
and equation.
____EXPRESSION____________
____EQUATION_______
-7x + 6
-3x + 2 = 8
___VARIABLE__
___COEFFICIENT_________
_TERM_ __CONSTANT/TERM____
Phrases to Expressions
Match each phrase to the expression. You will not use all the letters. You can use letters more than once!
𝑥
2
_D____ 1. 2 more than a number
A.
__H___2.
___A__3
__F___4.
__G___5.
__I___6.
B.
C.
D.
E.
F.
x-2
2+x
x+2
x2 (NEVER write the variable 1st in multiplication)
2-x
__H___7. Twice a number
G.
2
𝑥
__B___8. Two less than a number
H. 2x
I. x²
The product of 2 and a number
Half a number
The difference in 2 and a number
The quotient of 2 and a number
A number squared
Simplify the Expressions
(Add the terms that share a variable, the operation sign directly in front of the term is its sign)
1.
-7x + 6y -19 - 3x + 4y +12
-10x +10y-7
2.
c + 2d + 3c - 3d
4c – d
Properties
Identify the mathematical property that each expression represents by writing C for commutative property, A for Associative
Property, I for identity property and D for distributive property.
_A_1. c+(d +e) = d +(c + e)
_I__2. h + 0 = h
_C_3. jk = kj
_C_4. a + (b + c) = (b+c) +a
__D__5. 9(k + 9) = 9k + 81
__C__6. 8 + 4 = 4 + 8
__D__7. 4(3x + 7)= 12x + 28
__I__ 8. 1g=g
Distributive Property
Use the distributive property to simplify the expressions. (Multiply the number on the outside by all terms inside the
parenthesis) *Remember the sign in front belongs to the term, follow integer rules!
1. -3(2x + 6)
2. 2(-5x + 4 )
3. -2( -6x – 3y + 2)
4. 5(-2x – y + 7)
-6x -18
-10x + 8
12x +6y -4
-10x -5y + 35
Factor the following equations
(Find the greatest common factor for the terms, divide both terms by the GCF, and write the expression using
distributive property)
1. -6x + 32
2. - 9y – 33
2(-3x + 16) or -2(3x- 16)
3(-3y -11) or -3(3y + 11)
Solving 1-Step Equations
1. x – 7 = - 87 + 7
+7 =
x= -80
2. -3x = -39
-3
-3
3.
𝑥
= 5(-12)
−12(−12)
x = -60
4. x + -5.6 = 7.9 - -5.6
- -5.6
x = 13
2
3
4
x=-
12
16
=-
5.
2
3
x=-7
4
2
÷4
÷4 -7x2
x = 13.5
6
7
Solving 2-Step Equations
1. -3x + 7 = 85 - 7
-7
-3x 78
2.
𝑥
−7
- 4 = -13 + 4
3.
𝑥
−3.7
+ 3.4 = -12.5 – 3.4
+4
𝑥
(-7)
−7
𝑥
(-3.7)
−3.7
-11(-7)
-3 -3
x = -26
x = 77
Write an expression for each real world scenario.
-15.9(-3.7)
x = 58.83
1. A bike rental shop charges a $25 dollar deposit for renting a bike and $4 additional dollars for each day. Write an
expression to represent the cost of renting a bike for d days.
4d + 25
2. A car salesman’s will receive a 15% bonus on his s salary in the month of January. Write an expression to show
how much he will get paid in January. s + .15s = 1.15s
Extended response (To earn full credit on an extended response question, make sure to explain each step clearly
and in complete sentences. Use mathematical vocabulary and double check for accuracy. Reread you explanation to
make sure that a person who may be unfamiliar with the concept could follow your explanation.)
Explain how to simplify an expression by combining like terms. Use the expression below to show the process. Be
sure to clearly explain each step in detail. -4x + 2y – 6x + 8 – 10 – 5y = -10x -3y - 2
To combine like terms you must add terms that share a variable. You must remember that the sign of the term is
the sign located directly in front of the term. First I combined the coefficients, -4x and -6x which equals -10x. I then
combined +2y and -5y which equals -3y. You must remember to follow the integer rules when combining terms.
Lastly I added the constants +8 and -10 which equals -2. After combining the like terms, you put all the simplified
terms together which resulted in the simplified expression -10x – 3y -2 .
Write an equation for the real world scenario and then solve. A field trip costs $16.00 per student s and an additional
$200 for bus transportation. If 54 students are going on the trip, taking 1 bus, how much will the trip cost?
16s +
200 16(54) + 200=$ 1064
Review
-52(32) -1664
101- 107 -6
98 – (-75) 173
−108
−12
9
-32 – 81 -113
Draw a model on a number line to represent -6 + 8