Section A Understanding Variables and Expressions
2-1
2-2
2-3
Variables and Expressions
Translating between words and math
Translating between tables and expressions
Section A Quiz
Section B Understanding Equations
2-4 Equations and Their Solutions
2-5 & 2-6 Addition Equations and Subtraction Equations
2-7 & 2-8 Multiplication Equations and Division Equations
Section B Quiz
Section C A Deeper Look at Expressions
Lesson 1
Lesson 2
Parts of an Expression
Generate and Identify Equivalent Expressions
Sections C Quiz
Algebra Unit Test
Keep track of your progress below.
Put a check mark in the box when you can do the following!
☐ I can write algebraic expressions from verbal
descriptions
☐ I can identify parts of an expression using mathematical
terms such as sum, term, product, factor, quotient,
coefficient, and quantity
☐ I can evaluate expressions by substituting values for
variables
☐ I can evaluate expressions in real-world situations
☐ I can determine if a given number makes an equation
true by using substitution
☐ I can write algebraic expressions to represent
mathematical problems
☐ I can write algebraic expressions to represent real-world
problems
☐ I can write a one-step equations with non-negative
rational numbers representing a real-world situation
☐ I can solve a one-step equation with non-negative
rational numbers representing a real-world situation
2-1 Variables and Expressions
Vocabulary
_______________ – a symbol used to represent a quantity that can change
_______________ – a value that does not change
_______________ – a mathematical phrase that contains operations, numbers, and/or
variables
_________________________ – an expression that contains at least one variable
_______________ – to find the value of a numerical or algebraic expression
Examples of algebraic expressions:
Addition
Subtraction
Multiplication
Division
Is the following a variable (V) or a constant (C)?
1. Number of days in January _____
4. Price of a calculator _____
2. Number of students in a school _____
5. Number of inches in a foot _____
3. Number of people in a state _____
6. Number of giraffes in a herd _____
Example 1: Evaluating Algebraic Expressions
EVALUATE each expression to find the missing values in the tables.
w
55
w ÷ 11
5
(55 ÷ 11= 5)
66
77
n
1
4n + 62
2
3
Evaluate each expression for x = 1, 2, and 3
x
x+5
x
11 - x
Evaluate each expression for x = 2, 5, and 8
x
4x
40
𝑥
x
Example 2: Evaluating Expressions with Two Variables
A rectangle is 2 units wide. What is the area of the rectangle if it is 4, 5, 6, or 7 units long?
l
w
4
2
5
2
6
2
7
2
lxw
Think and Discuss
1. Name a quantity that is a variable and a quantity that is a constant.
2. Explain why 45 + x is an algebraic expression.
2-2 Translating Between Words and Math
Example 1: Social Studies Applications
A. The Nile River is the world’s longest river. Let n stand for the length in miles of the Nile. The
Amazon River is 4,000 miles long. Write an expression to show how much longer the Nile is
than the Amazon.
B. Let s represent the number of senators that each of the 50 states has in the U.S. Senate.
Write an expression for the total number of senators.
Example 2: Translating Words into Math
Directions: Put the words from the box on the lines in the correct column below.
product
groups of
decreased by
difference
quotient
more than
take away
less than
increased by
of
KEY WORDS
ADDITION
SUBTRACTION
MULTIPLICATION
1. minus
1. sum
DIVISION
1. divided by
1. times
2. subtracted from
2. plus
3. ______________
3. ______________
4. ______________
4. ______________
5. ______________
2. ______________
2. multiplied by
3. ______________
4. ______________
5. ______________
6. ______________
EXAMPLES
Operation
+
-
x
Algebraic
Expression
x + 28
k – 12
8w OR 8 • w
8(w) OR (8)(w)
Words
28 more than x
the sum of x and 28
k minus 12
12 less than k
÷
n ÷ 3 OR
𝑛
3
8 times w
n divided by 3
8 groups of w the quotient of n and 3
REMEMBER:
It is helpful to put a number in place of the variable so that you can check if your
answer is REASONABLE!
Directions: Write each phrase as a numerical or algebraic expression
1. 79 minus 15
__________
2. 28 more than 37
3. 8 groups of 4
__________
__________
4. product of 20 and k
5. difference of g and 6
6. the quotient of n and 3
__________
__________
__________
10. c tripled
__________
11. 3 increased by s
__________
12. m to the fourth power
13. j squared
__________
__________
14. r cubed
__________
15. half of b
__________
7. 5 more than f
__________
16. one third of a
8. j less than 5
__________
17. Caroline made f batches of 12 cookies. How
many did she bake? __________
9. 20 less than y
__________
__________
Example 3: Translating Math into Words
Directions: Write TWO phrases for the expressions below.
A. (34) (7)
B. a – 45
1) Joe collected 200 coins. He is planning to sort them into r containers, with an equal
number of coins in each container. Circle the expression that tells how many coins will be in
each container.
a) r + 200
b) 200 ÷ r
c) 200 – r
d) 200r
2)Write f more than 47 as an algebraic expression: ________________________
3)Write 18 less than g as an algebraic expression: _______________________
Think and Discuss:
1. Tell how to write each of the following phrases as a numerical or algebraic expression: 75
less than 1,023; the product of 125 and z.
2. Give two examples of “a ÷ 17” expressed with words.
Writing Algebraic Expressions Practice
Write each situation as an algebraic expression
1. Bernadette walked for 10 minutes.
Then she walked for a few more
minutes. How many minutes did she
walk in all?
3. There are 8 pencils in each pack of
pencils. A teacher ordered some packs
of pencils. How many pencils will the
teacher receive?
2. At night, the daytime temperature
decreases by 7 degrees. What is the
temperature at night?
4. The Simpson family drove for 4 hours.
At what rate did they drive?
(HINT: Rate = miles/hour)
Write an expression for each situation. Use n when a variable is needed.
5. the quotient of a number and 8
7. 12 less than 30
6. Harry ran 2 more miles more this week
than last week.
8. Elena bought 5 pounds of oranges.
What was the cost per pound?
Circle the letter of the expression that matches each statement below. THINK … DON’T GUESS!!!!
9. Multiply 2 and 7. Then, subtract h.
12. Subtract 6 from e. Then, divide by 3.
a. 2 x (h - 7)
b. 2 x h - 7
a. (e - 6) ÷ 3
b. 6 - e ÷ 3
c. 2 x 7 - h
d. 2 x (7 - h)
c. (6 - e) ÷ 3
d. e - 6 ÷ 3
10. Subtract 6 from e. Then, divide by 3.
a. (e - 6) ÷ 3
b. 6 - e ÷ 3
c. (6 - e) ÷ 3
d. e - 6 ÷ 3
13. Divide 11 to the 9th by 3; then add 76
a.
b.
c.
d.
11. Three times eight to the fifth power.
a. 38 × 5
b. 38 × 5
c. 3 × 8 × 5
d. 3 × 85
14. Five more than the quotient of a number
and 9.
a.
b.
c.
d.
Writing Algebraic Expressions HOMEWORK
Write each situation as an algebraic expression
1. Corinne had $20. She spent some
money for lunch. How much money did
she have left?
2. Martha makes some potholders to sell
at a craft fair. She sells them for $5
each. How much money does she earn
by selling the potholders?
Write an expression for each situation. Use n when a variable is needed.
3. The temperature increased by 10
degrees from the morning until noon.
5. The depth of the lake was reduced by
1.5 feet.
4. Ken earns $5 for every hour he works.
6. Maxine earned 3 points for every
correct answer on a test.
Circle the letter of the expression that matches each statement below. THINK … DON’T GUESS!!!!
7. Subtract m from 9. Then, add 4.
11. Four times nine to the fifth.
a. 9 - 4 + m
b. 9 - m - 4
a. 4 × 9 × 5
b. 49 × 5
c. 9 - m + 4
d. m - 9 + 4
c. 49 × 5
d. 4 × 95
8. Multiply f and 6. Then add 9.
12. Five times a number plus eleven.
a. f × 9 + 6
b. (f + 6) × 9
a. 5 + n + 11
b. 5n + 11
c. f × 6 + 9
d. f × (6 + 9)
c. 5/9 + 11
d. 5 + 11n
9. Multiply 6 and 8. Then, divide by p.
a. 9 - 4 + m
c. 9 - m + 4
13. Add 24 and 14; then, raise the sum to the
5th power.
b. 9 - m - 4
a. (24 × 14)5
b. (24 + 14) × 5
c. 24 + 145
d. (24 + 14)5
d. m - 9 + 4
10. Add 6 and b. Then, multiply by 2.
a. (6 + b) × 2
b. b + 6 × 2
c. 6 × (2 + b)
d. 6 + b × 2
14. Raise the product of 38 and 8 to the power
of the sum of 3 and 5.
a. (38 ÷ 8)3 + 5
b. (38 ÷ 8)(3 + 5)
c. (38 × 8)(3 × 5)
d. (38 × 8)(3 + 5)
2-3 Translating Between Tables and Expressions
(Input / Output Tables)
Example 1: Writing an Expression
A.
Reilly’s Age
Ashley’s Age
9
11
10
12
11
13
12
14
n
When Reilly’s age is n, Ashley’s age is _____________
B.
Eggs
Dozens
12
1
24
2
36
3
48
4
e
When there are e eggs, the number of dozens is e ÷ 12, or ________
Example 2: Writing an Expression for a Sequence
Write an expression for the sequence in the table.
Position
1
2
3
4
5
Value of Term
3
5
7
9
11
n
Look for a relationship between the positions and the values of the terms in the sequence. Use
guess and check.
Practice: Write an expression for the missing value in each table
#1
#2
Go-Carts
1
2
3
4
Wheels
4
8
12
16
Position
1
2
3
4
5
Value of
Term
9
10
11
12
13
#3
Players
Soccer
Teams
22
#4
n
Weeks
Days
2
4
28
44
4
8
56
66
6
12
84
88
8
16
112
x
#5
x
n
Position
1
2
3
4
5
Value of
Term
7
12
17
22
27
n
#6 Which expression describes the sequence in the table?
Position
1
2
3
4
5
Value of
Term
6
11
16
21
26
A) n + 5
B) 5n + 1
C) 6n
n
D) 6n – 1
Think and Discuss:
1. Describe how to write an expression for a sequence given in a table.
2. Explain why it is important to check your expression for all of the data in the table.
Translating Between Tables and Expressions
HOMEWORK
Circle the letter of the correct answer.
1. Which sentence about the table is true?
Cars
1
2
3
c
2. Which sentence about the table is not true?
Brett’s Age
10
11
12
b
Wheels
4
8
12
4c
A The number of wheels is the number of
cars plus 4.
Joy’s Age
11
12
13
b1
F Joy’s age is Brett’s age plus 1.
B The number of wheels is the number of
cars minus 4.
G When Brett’s age is b, Joy’s age is b  1.
C The number of wheels is the number of
cars divided by 4.
J
H Add 1 to Brett’s age to get Joy’s age.
D The number of wheels is 4 times the
number of cars.
Subtract 1 from Brett’s age to get Joy’s
age.
Write an expression for the missing value in each table.
3.
Motorcycle
1
2
3
m
Wheels
2
4
6
4.
Marbles
15
20
25
m
Bags
3
4
5
5.
Bicycles
1
2
3
b
Wheels
2
4
6
6.
Ryan’s Age
14
16
18
r
Mia’s Age
7
9
11
7.
Minutes
60
120
180
m
Hours
1
2
3
8.
Bags
3
4
5
b
Potatoes
21
28
35
9.
Game
1
2
3
g
10.
Cards
52
104
156
Paper Clips
250
500
750
c
Boxes
5
10
15
Write an expression for the sequence in the table.
11. Position
Value of Term
12. Position
Value of Term
13. Position
Value of Term
14. Position
Value of Term
1
2
3
4
5
3
4
5
6
7
1
2
3
4
5
5
9
13
17
21
1
2
3
4
5
8
13
18
23
28
1
2
3
4
5
0
1
2
3
4
15. A rectangle has a width of 6 inches. The
table shows the area of the rectangle for
different widths. Write an expression that
can be used to find the area of the rectangle
when its length is l inches.
16. What is the relationship between the
number of bags and the number of coins?
_______________________________________
_______________________________________
n
the answer is
not 8
n
the answer is
not 25
n
the answer is
not 33
n
Width (in.)
6
6
6
6
Length (in.)
8
10
12
l
Bags
3
5
7
b
Coins
18
30
42
?
the answer is
not 5
Area (in.2)
48
60
72
17. Look at the table below.
Position
1
2
3
4
5
n
Value of Term
1
3
5
7
9
?
What is the relationship between the positions and the values of the terms in the sequence?
2-4 Equations and their Solutions
Vocabulary
_______________ – a mathematical statement that two expressions are equal
_______________ – a value or values that make an expression true
Is the following an EQUATION or an EXPRESSION?
a. 15 + y = 20 __________________________
b. (m - 4) x 7 ____________________
An equation is like a scale with the equal sign in the middle
Both sides have the same value.
They must always stay in balance.
2+6 = 5+3
The SOLUTION to this equation is:
2+x =
x = ______
5
EXAMPLE 1: Determining Solutions of Equations
Determine whether the given value of the variable is a solution. YES or NO!
5𝑦 = 40, 𝑦 = 8
ℎ − 12 = 24 , ℎ = 12
𝑟 + 20 = 35, 𝑟 = 10
5 + 𝑑 = 5, 𝑑 = 0
30
𝑧
= 3 ,𝑧 = 6
5𝑤 = 20 , 𝑤 = 4
Circle the equation that is true for y = 3
a) 12 = 4 + y
b) 12 = 4 – y
For which value of the variable is the equation true?
a) w = 3
b) w = 9
c)
12
4
y
d) 4 = 12 y
3w + 5 = 17
c) w = 4
d) w = 2
Example 2: Life Science Application
You can use equations to check whether measurements given in different units are equal:
One science book states that a male giraffe can grow to be 19 feet tall. According to another book, a
male giraffe may grow to 228 inches. Determine if these two measurements are equal.
What do we need to know?_______________________________________
Write it algebraically:
Substitute and solve:
________________________
_________________________
PRACTICE
Determine whether the given value of the variable is a solution. YES or NO!
𝑐 + 23 = 48 for 𝑐 = 35
96 = 130 − 𝑑 for 𝑑 = 34
75 ÷ 𝑦 = 5 for 𝑦 = 15
𝑧 + 31 = 73 for 𝑧 = 42
85 = 194 − 𝑎 for 𝑎 = 105
78 ÷ 𝑛 = 73 for 𝑛 = 5
Kent earns $6 per hour at his after-school job. One week, he worked 12 hours and received a
paycheck for $66. Determine if Kent was paid the correct amount of money.
Think & Discuss:
1. Tell which of the following is the solution of y ÷ 2 = 9 :
y = 14, y = 16, or y = 18. How do you know?
2. Give an example of an equation with a solution of 15.
2-5 & 2-6 Addition and Subtraction Equations
Vocabulary
_______________ _______________ – operations that undo each other: addition and subtraction,
or multiplication and division.
Taking away 14 from both sides of the scale is
the same as subtracting 14 from both sides of
the equation.
Example 1: Solving Addition Equations
Solve each equation. Check your answers.
𝑥 + 62 = 93
81 = 17 + 𝑦
52 + 𝑏 = 71
𝑝−2=5
40 = 𝑥 − 11
𝑥 − 56 = 19
Example 2: Social Studies Application
Johnstown, Cooperstown, and Springfield are located in that order in a straight line along a highway.
It is 12 miles from Johnstown to Cooperstown and 95 miles from Johnstown to Springfield. Find the
distance d between Cooperstown and Springfield.
distance between
Johnstown and
Springfield
________
=
distance between
Johnstown and
Cooperstown
+
=
________
+
distance between
Cooperstown and
Springfield
_________
Practice: Solve each equation. Check your answers.
1. 𝑥 + 19 = 24
2. 𝑦 − 18 = 7
3. 10 = 𝑟 + 3
4. 8 = 𝑛 − 5
5. 𝑠 + 11 = 50
6. 𝑎 − 34 = 4
7. 𝑏 + 17 = 42
8. 𝑐 − 21 = 45
9. 12 + 𝑚 = 28
10. Write “21 is 5 subtracted from y” as an equation. Then solve.
Write an equation for each statement. Then solve.
The number of eggs e increased by 3 equals 14.
The number of new photos taken p added to 20 equals 36.
When 17 is subtracted from a number, the result is 64.
NAME ______________________ 
Adding and Subtracting Equations Practice #1
Solve each equation! Check your work. Circle your answers.
1. x + 12 = 16
check
2. 23 + g = 34
check
3. r – 57 = 7
check
4. 11 = x – 25
check
5. 52 + y = 71
check
6. 87 = b + 18
check
7. a – 6 = 15
check
8. g – 71 = 72
check
9. m + 25 = 47
check
10. Write an equation for the following
statement. Then solve the equation.
The number of skittles (s)
increased by 5 equals 20
NAME ______________________ 
Adding and Subtracting Equations Practice #2
Solve each equation! Circle your answers.
1. x + 18 = 44
2. x – 12 = 6
3. 75 + x = 97
4. x + 47 = 144
5. x – 23 = 63
6. x – 72 = 2
7. x – 17 = 51
8. 66 + x = 129
9. x – 11 = 67
10. x + 52 = 72
11. 57 + x = 75
12. 82 + x = 116
13. x – 57 = 23
14. 85 + x = 127
15. 83 + x = 150
16. x – 19 = 46
17. x – 28 = 45
18. 91 + x = 177
19. Write an equation for the following statement. Then solve the equation.
The number of skittles (s) decreased by 13 equals 20
2-7 & 2-8 Multiplication & Division Equations
Example 1: Solving Multiplication & Division Equations
Solve each equation. Show ALL work. Check your answers.
3𝑥 = 12
8 = 4𝑤
𝑦
12 = 4
5
=4
𝑧
135 = 3𝑦
𝑐
12
=8
Marcy spreads out a rectangular picnic blanket with an area of 24 square feet. Its width is 4 feet.
What is its length?
(Remember A = l x w  AREA = LENGTH x WIDTH)
Millipedes can have up to 752 legs! They have 4 legs per segment. How many segments could the
millipede have?
Carl has n action figures in his collection. He wants to place them in 6 bins with 12 figures in each
bin. Write and solve an equation.
Practice: Solve each equation. Check your answers.
1. 12𝑝 = 36
𝑧
2.
𝑦
4
=3
3. 114 = 6𝑎
4. 14 = 2
5. 64 = 8𝑛
7. 20 = 5𝑥
8. 12 = 3
𝑗
6.
𝑟
9
=7
9. 9𝑧 = 135
The area of a rectangle is 42 square inches. Its width is 6 inches. What is the length?
A = length x width
Taryn buys 8 identical glasses. Her total is $48 before tax. Write and solve an equation to find out
how much Taryn pays per glass.
Paula is baking peach pies for a bake sale. Each pie requires 2 pounds of peaches. She bakes 6
pies. Write and solve an equation to find how many pounds of peaches Paula had to buy.
NAME ______________________ 
Multiplying and Dividing Equations Practice #1
Solve each equation! Check your work. Circle your answers.
1. 7x = 56
check
2. 11g = 99
check
c
4
9
check
4.
x
 15
4
check
5. 27 = 3w
check
6. 132 = 12m
check
8.
check
10.
3.
7.
9
y
5
9. 6y = 114
k
1
28
j
 10
20
check
check
check
11. The area of a rectangle is 63 square feet. Its width is 3 feet. What is its length?
NAME ______________________ 
Multiplying and Dividing Equations Practice #2
Solve each equation! Check your work. Circle your answers.
1. 7x = 56
4.
c
4
9
7. 27 = 3w
10.
9
y
5
13. 6y = 114
2. 11g = 99
5.
x
 15
4
8. 132 = 12m
3. 5x = 125
6.
x
 11
3
9. 7g = 77
x
9
8
11.
k
1
28
12.
14.
j
 10
20
15. 10k = 130
16. The area of a rectangle is 84 square feet. Its width is 4 feet. What is its length?
Section C - Lesson 1: Parts of an Equation
Vocabulary
_______________ – a part of an expression that may be a constant number, a variable by itself, or
any grouping of numbers and/or variables combined by multiplication and/or division.
_______________ – a value that does not change
_______________ – the number part when a number and a variable are combined by multiplication
Defining a Term in an Expression
The following expressions are examples of terms:
-
a variable by itself → _____
- a constant → _____
-
grouping of a number and a variable combined by multiplication → _____
-
grouping of a number and a variable combined by division → _____
-
grouping of a number and two variables combined by multiplication → _____
-
grouping of a number and a variable combined by multiplication and division → _____
Counting the Terms in an Expression
Terms in an expression are separated by ____________ and ____________ signs.
The expression 3x + 2y - 7 has ____ terms.
They are ______, ______, and ______.
𝑎
The expression 6xy - 4 + 3n - 5 has ____ terms. They are ___________________________________
Parenthesis can serve as a grouping symbol, so they make expressions into one term.
Example:
3 + 4 has ____ terms
(3 + 4) has ____ term
How many terms are in the expression 2(x + 5) - 9
→ ___
PRACTICE
How many terms do the following expressions have? Put a box around each term.
𝑚
1. 3x - 2y → ___
2. 4m - 7 +
4. (3 + a) → ___
5. 3(n - 5) + 7y → ___
2
→ ___
3. 7abcdef → ___
6. -2(3x + 5) + 10(a + b) → ___
Identifying the Coefficient of an Expression
When a number and a variable (or variables) are combined by multiplication, the number is called the
coefficient. When we write a variable with a coefficient, we do not use any kind of multiplication
symbol.
𝑛 2𝑛
What is the coefficient of the terms: 4n, 3xy, -2.5n, n, 6,
4n → _____
3xy → _____
3
, and 15.
-2.5n → _____
n → _____ (n is equivalent to 1 x n)
𝑛
6
→ _____
𝑛
1
(6 is equivalent to 6 𝑛)
15 → ________
2𝑛
3
2𝑛
2
→ _____ ( 3 is equivalent to 3 𝑛)
(15 is a ______________, so it ____________ have a coefficient)
PRACTICE
Identify the coefficient in the terms below
1. 5ab → _____
2. w → _____
3.
3𝑛
4
→ _____
Parts of an Equation HOMEWORK
Identify the coefficient in each term.
1. 9r → _____
2.
3
8
𝑡 → _____
3. -3m → _____
4. abc → _____
Identify the coefficient of n in each expression.
5. 9m + 3n → _____
8. 6.7m + 3.03n → _____
6. 2n + m + 3 → _____
1
1
9. 2 + 1 2 𝑛 + 2 2 𝑚 → _____
7. -6n + 2 → _____
10. 2m +
𝑛
5
→ _____
How many terms do the following expressions have? Hint: Put a box around each term.
3
11. 9n - 3 → _____
12. 6a + 2b + 4c - 5 → _____
14. 103mnprs → _____
17.
(9+𝑛)
5
15. 5(3n - 2)(8 - 2b) → _____
4
- n + 4n - 5(n + 4) → _____
13. 16r → _____
16. (9 + a) → _____
18. -3(a - b) + 2c - 4(d + 4) → _____
Use parentheses to change the number of terms in each expression.
19. Add parentheses to the expression below so it has only 2 terms.
9a + b + 7
20. Add parentheses to the expression below so it has only 3 terms.
r + s x 7 + 3t + 5 x 3
Circle what is alike and underline what is different in each pair of terms.
21. 2k and 3k
variables / coefficients
22.
3
4
3
𝑔 + 4ℎ
variables / coefficients
Solve the problem below
23. The teacher says that 2m2 + 3n has two terms, 2m2 and 3n. Why is 2m2 considered one term?
Justify your answer →
Section C - Lesson 2: Generate and Identify Equivalent Expressions
Vocabulary
__________ __________ – terms whose variables are the same
Recognizing Equivalent Expressions
Which pair of the following expressions are equivalent expressions?
7(x - 4) and 7x - 4
OR
5(n + 7) and 5n + 35
The distributive property can be used to help determine if two expressions are equivalent.
Apply the distributive property to each of the expressions:
7(x - 4)
5(n + 7)
AND
_______________________ are equivalent expressions
Apply the distributive property to the following expressions
3x + 15
5n - 45
AND
PRACTICE
Use the distributive property to write the expressions without parentheses.
1. 2(x - 5) → ____________
2. 9(2n + 8) → ____________
3. 15(w - 2) → ____________
Use the distributive property to write the expressions using parentheses.
4. 3x + 12 →____________
5. 11n - 55 → ____________
6. 9x - 18 → ____________
Decide whether the expressions in each pair of expressions are equivalent. Circle your choice!
7. 4(x + 6) and 4x + 6
equivalent / not equivalent
8. 7(y + 8) and 7y + 56
equivalent / not equivalent
9. 9n - 54 and 9(n - 4)
equivalent / not equivalent
Combining Like Terms
We know that an expression such as 7 + 5 can be combined into one term, 12, since both terms in
the expression are constant numbers. Since both terms are the same type, they are called like terms,
and may be combined by adding or subtracting.
In the expression 5x + 8, the two terms are ______________. One term has a variable, x, and the
other is a constant term. These are UNLIKE terms, and cannot be combined further.
In the expression 8n + 3n, the two terms are the _________. They both have the variable ____,
therefor are LIKE TERMS. Like terms can be combined by adding the coefficients and keeping the
variable the same.
8n + 3n = _______
Can the terms 5x and 10y be combined?
More examples: Combine the like terms
1. 12y - 7y = _______
2. 6x + 2x + 5x = _______
4. 5x + 2y + 5x = _________
3. 2g + 9g = _______
5. 3x + 4y + 5 + 2x + 3y = _______________
PRACTICE
6. 3x + 7 - 2x = ____________
7. 4y - 2y + 5 - 2 = ___________
8. 8y - 2x = _________
Use the distributive property and combining like terms to write an equivalent algebraic expression.
9. 2(3x - 4) + 3x = ________________
10. 5(3y + 2) + 4y - 8 = __________________
Generating and Identifying Equivalent Expressions
HOMEWORK
Use the distributive property to write the expressions without parentheses.
1. 6(a + 5) → ____________
2. 3(2b - 8) → ____________
3. 25(w - 2) → ____________
Use the distributive property to write the expressions using parentheses.
4. 2c + 8 → ____________
5. 3n - 12 → ____________
6. 15x - 10 → ____________
Decide whether the expressions in each pair of expressions are equivalent. Circle your choice!
7. 8(n - 3) and 8n + 24
equivalent / not equivalent
8. (p + 3)2 and 2p + 32
equivalent / not equivalent
9. 10v + 90 and 10(v + 9) equivalent / not equivalent
Combine the like terms
10. 10y - 4y = _______
13. 4x + 3y + 6x = _________
15. 4x + 8 - x = ____________
11. 7x + 3x + 9x = _______
12. 3g + 8g = _______
14. 4x + 3y + 6 + 4x + 3y = _______________
16. 5y - 2y + 7 - 2 = ___________
17. 5y - 2x = _________
A square has a side length of s + 16. A rectangle has a length of s + 25. Find the perimeter of each.
Are the perimeters the same? (Reminder: Perimeter is the distance around the figure)
Justify your answer →
# ___________
Name _____________________________
Expressions Practice
Evaluate the expressions using the given value for the variable. Show all work!
1. 7x2
when x = 5
2. 2x2 + 5x
when x = 6
3. 3x4 - 4x3 + 5x
when x = 2
Apply the distributive property to the following expressions
4.
5(4x + 8)
5.
7(5x + 3y + 9)
6.
10(9x – y + 3)
Use the distributive property and/or combining like terms to write an equivalent algebraic expression
7. 8x + 5y + 4x + 6 + 3y
8. 9(5x + 10) – 7x
9. 7(6x + 11) + 13x -14
10. 5(7x + 9) – x
11. 5(4y + 11z) – 55z
12. 4(5a +3b - 7) + 8(4a)
BONUS – Solve for x
5(x + 8) + 2(3x) = 172
# ___________
Name _____________________________
Expressions Homework
Evaluate the expressions using the given value for the variable. Show all work!
1. 3x2
3. 4x2 + 3x
2. 5x3
when x = 3
when x = 2
4. 2x4 - 2x3 + 2x
when x = 5
when x = 2
Apply the distributive property to the following expressions
5.
4(3x + 7)
6.
6(4x + 2y + 8)
7.
9(8x – y + 2)
Use the distributive property and/or combining like terms to write an equivalent algebraic expression
8. 7x + 4y + 3x + 5 + 2y
9. 8(4x + 10) – 6x
10. 6(5x + 10) + 12x -13
11. 4(6x + 9) – x
12. 6(5y + 12z) – 72z
13. 3(4a +2b + 6) + 7(3a)
Expressions Challenge Problems
Evaluate the expressions using the given value for the variable. Show all work!
1. 9x3
when x = 3
2. 8x2 + 12x
when x = 9
3. 3x4 - 2x3 + 5x
when x = 3
Apply the distributive property to the following expressions
4.
15(4x + 8)
5.
5(15x + 13y + 19)
6.
12(7x – y + 10)
Use the distributive property and/or combining like terms to write an equivalent algebraic expression
7. 18x + 15y + 24x - 6 - 13y
8. 13(3x + 10) – 13x
9. 11(6x + 12) + 13x -54
10. 15(3x + 12) – x
11. 4(4y + 50z) – 84z
12. 5(6a +4b - 8) + 9(7a +5b + 9)
BONUS – Solve for x
6(x + 7) + 4(2x + 8) = 284