Unit 1: Introduction to ALGEBRA
REMEMBER
You cannot ADD or SUBTRACT unlike terms
EXAMPLE:
6x – 4 + 8x
*Bring like terms together
6x + 8x – 4
14x – 4
Give an algebraic expression for the perimeter
of each figure.


14x – 4 is the simplified expression, we cannot
subtract 14x & 4 because they are unlike, 14x
is a variable term & 4 is a constant term
[number only]
3x
5x
3x
2x
4n + 7


n
n+3
n+3
4x – 3
n
n
4x – 3
6n – 2


4n + 5
4x + 2
4n + 5
4x + 2
3x – 2
3x – 2
2x – 3
2n – 1
SIMPLIFY each of the following algebraic expressions.
*Remember, you can ONLY + & — LIKE terms!
a+a+a
 2b + 5b
 4a + 2a + 5
 x –x + x + 3
y+y+y+y+2+5
 3b + 2 – 2b – 3
 –8a + 2a + 5
 10b – 9b
 3a + 2a + 3x
 12a – 6a
 15x – 10
 2x + 8x
 x + 2x + 5x
 2a + 5 + 3a
 20a + 18 + 2a + 5
 –x + –7x
 8t – 12t
 –8a – 12a
 –18r – 12r
 –7a – 9a
 –10c + 2c
Translating Words into an Algebra Expressions
Example: the sum of three times a number and eight means 3x + 8
Write an algebraic expression for each statement.
 The sum of a number and six
______________
 The quotient of fifteen and a number
______________
 The difference between a number and twenty
 The product of seven and a number
______________
______________
 The difference between the square of a number and three _____________
 The sum of triple z and double n
______________
 One quarter of a number
______________
 Three times a number decreased by nine
______________
 Double a number less one hundred
______________
 Ten less than half a number
____________
Translating Words into an Algebra Expressions
Example: twenty less than triple a number means 3x – 20
Write an algebraic expression for each statement.
 The sum of double a number and two
______________
 The quotient of twice a number and three
______________
 The difference between fifty and a number
______________
 The product of ten and a number
______________
 The difference between five times a number and seven ___________
 The difference of triple x and double z
______________
 One third of a number
______________
 Six times a number decreased by fifteen
______________
 Triple a number less seventy
______________
 Nineteen less than one quarter of a number
____________
Translating Words into an Algebra Expressions
Example: Fifteen less double a number means 15 – 2n
Write an algebraic expression for each statement.
 The sum of five and seven times a number
______________
 Ten more than two times a number
______________
 Eight less than five times a number
______________
 The product of three times a number and four
______________
 Eleven less than four times a number
______________
 The square of the sum of six times and two
______________
 One fifth of a number
______________
 The sum of a number and twice the same number
______________
 The sum of an even number & the next even number ______________
 The sum of a number & the next two consecutive numbers __________
SIMPLIFY each of the following; SIMPLIFY means to combine LIKE TERMS.


6x + 3x

–
6n + –5n

15s + –4s
–
7b – –4b

9x – –2x


1 + 3x – 5x + 7

x – 1+ 4x – 6

7x + 8 + 3x – 3

8 + 2x + x – 3
 7x – 10 – 3x + 5

–
–



–
5n – 8n
4x – 6 – 4x + 1
6x + 4 – 3x – 9

–
10 – 4x + 5x +6

3s + 6s – 13 + 5
2t – 10 – 6t

8 – 3x – 7x
6n + 3 + 9 – 2n
Algebraic Expressions in Word Problems
 The rate for a taxi is $5.00 plus $1.35 for each kilometer traveled. Write a simplified algebraic
expression to represent the cost of a taxi ride for x kilometers.
 Jason sold x yearbooks the first week, he sold double that in the second week and during the
third week he sold 5 less than during the second week. Write an algebraic expression for each
week and then write a simplified expression to represent the total number of yearbooks that
Jason sole.
Week #1: ____________
Simplified expression:
Week #2: ____________
Week #3: ____________
 Pencils cost p¢ each [taxes included]. How many pencils can be purchased for $d?
 If a represents a person’s age in years, give an expression to represent the person’s age:
a) in months?
b) in days?
 If a student has x classes in n days, how many classes does the student have per day?
 Todd weighed x kg and lost n kg in each of four consecutive weeks. Give an algebraic
expression to represent Todd’s weight after four weeks.
 If there are x boys and n dogs in the park, write an algebraic expression to represent the total
number of feet in the park.
 Write an algebraic expression to represent your average on math tests where you scored, x %,
n % and y %.
STEPS to REMEMBER
EXAMPLE:
(6x – 4) – (8x + 3)
*Notice minus sign between brackets
Step 
6x – 4 – 8x – 3
Remove brackets & make necessary changes
Step 
6x – 8x – 4 – 3
*Bring LIKE TERMS together
Step 
2x – 7
*Simplified, cannot subtract unlike terms!
SIMPLIFY each of the following:

(2x + 4) + 6

(3x + 1) + 3x


x + 3 – 2x

8x + 5x + 5 – 2


(5x + 4) – (2x + 2)

(8x + 7) – (9x + 3)
(x + 3) + (4x + 2)
(6x – 5) + (x – 2)


(4x – 2) + 4

11x – (9x – 4)
(8x – 10) – (7x – 12)

(2x – 5) – (9 – 7x)

14x – (20x + 3)

(3x – 1) + (5x – 4)

(x + 3) – (3x + 1)

(x + 1) + (2x + 4)

(x – 2) – (2x – 3)

2x  4 + 3x + 8  5x

(4x – 7) – (8x – 9)

12x  9 + 7x + 15  15x

(6x – 3) – (11x – 10)
REMEMBER: You CAN multiply &
divide unlike terms
EXAMPLE :
9  15x
135x
*Multiply the integers, then include
variable & you have the expression
Simplifying Algebraic Expressions
MULTIPLICATION & DIVISION
56x  8
7x
*Divide the integers, then include variable
& you have the expression
EXAMPLE :
Remember: You can MULTIPLY or DIVIDE unlike terms!

7 • –6s

–
5x • –9


15n ÷ –5



6 • 2x

2(4x + 3)

(15x + 9)  3

–
 64m
 16


-
4 • –3x
–
84x ÷ 12

–
1(5x – 9)

4(4x – 2)
(25 x  10)
5

(–21 – 14x)  7
–
–
3x • 5
8 • –9x

9 • –15s


24n ÷ –8


9 • 6x

4(5x + 6)




–
3(7x + 4)

(12 x  33)
3

–
3n • –12

 60m
 10

–
3x • 14

–
7(2x – 9)

8(3x – 2)
–
1(8x – 7)

–
(20x – 35)  5

–
–
–
–
8 • 7x
81x ÷ 9
12 • –9x
5(9x – 12)
(54  18 x)
9

2(x – 8) – 3(4x – 2)

2(4x + 5) – 3(x + 2)

3(2x – 5) + 4(x + 1)

7(3x + 2) + 4(5x – 5)
9(2x – 3) – 8(4 – 5x)

4(6 + 8x) – 3(5 – 7x)

 5(2x + 1) – 4(x – 3) + 8(2 – 3x) – 4(3 – 5x)
Algebraic Expressions in Word Problems
 A repairman earns $x per hour plus $30 for traveling expenses. Write an algebraic expression
to represent a bill for 7 hours of work (excluding taxes).
 Sophie buys x packages of graph paper for $2.55 each (tax included). She pays with a $20
bill. Write an algebraic expression to represent the amount of change the cashier should give
back to Sophie.
 Jasmine pays $x for one dozen multigrain bagels. Write an algebraic expression to represent
the cost of 5 bagels.
 Sam sells tickets for the Hadley Junior High School Fall Talent Show, he sells (3x – 4) $3
tickets and (2x + 5) $4 tickets. Write a simplified algebraic expression to represent the
money Sam made.
Simplify each of the following expressions.
*Remember: The minus sign between the brackets means the sign inside the brackets changes to the opposite of
what is was, + to — or — to +

(5x + 4) – (x – 2)

(6 – 3x) + (x – 5x)

(4x + 5) – (3x – 2) – 6

9x + 5 – 7x

2 • –7x

3(2x – 6)

7x – 4(x + 2)

(12x – 6)  3

(10  6 x  8)
2

2(3x – 2) + 3(x + 5)
 Find the simplified algebraic expression for the perimeter of this polygon.
3x + 4
6–x
2x – 5
4x + 1
8 – 6x
B
I
N
G
O
ALGEBRA
BINGO
On the next page are a series of Algebraic Expressions and Phrases.
1. Cut out each of the expressions and phrases;
2. Match each phrase to an expression;
3. Glue 24 of the algebraic expressions to the above BINGO card;
4. Get some bingo chips & you are ready to play ALGEBRA BINGO! 
Algebra
Bingo
Card
Cut out each of these rectangles, there are 52 expressions and phrases in total.
After you cut them out, match the expression with the phrase. Once your teacher
has checked your matches you will glue JUST the expressions onto your BINGO card!

5 + x
6(x + 1)
2x – 5
4x + 3
6x – 1
x + 6
5 – 2x
3
( x  2)
2x - 6
x – 5
3x – 2
3x – 2n
Double a number
decreased by 5
The quotient of
three and a
number less two
Six less a number
6 – x
Nine minus five
times a number
Five more than a
number
Nine increased by
a number
Eight decreased by
a number
Two less than
three times
number
The difference
between triple x
and double n
Two times five
more than a
number
Five minus double
a number
Six less than
double a number
(x – 2)2
4x – 2
9 + x
8 – x
2 – 3x
2(x + 5)
x
6
Six times a number less
one
Product of six and a
number decreased by
1
Five times a number
plus 1
The square of a
number minus three
Four times a number
decreased by 2
A number divided by
six
Seven decreased by
two times a number
Three times a number
plus two
9 – 5x
Three more than
quadruple a number
7 – 2x
Eight less than the
cube of a number
3(x + 2)
Five less than a
number
The square of a
number decreased by
two
x2 – 3
5x + 1
A number
increased by six
x3 – 8
Two decreased by
three times a number
This pages needs to be torn
out and cut up to make your
ALGEBRA
BINGO
CARD

Unit 1 Extra Practice

10x – 8x + 7x + 2

(3y + 5) + (7y – 8)

(12a + 6) – (8a – 4)

11n + 5 – 9n + – (7n + 4)

7u – 2(u + 5)

3(y – 2) + 5(6 + y)

(4x + 10) – 2(3x – 5)

(24n – 16) ÷ 4

y + (y + 4) + (y – 4)

5(2x) + 3(3x – 4) – 6(7x)

(8x – 6) – (3x – 6)

(4s – 5) – (4s – 5)

(8 – n) + (n – 8) + 4n

3(5 – 2x) – 6(x + 8)