Writing Algebraic
Expressions
Objective:
Be able to write an algebraic
expression for a word phrase or write a
word phrase for an expression.
Warm Up
Evaluate each algebraic expression for the
given value of the variables.
1.)
7x + 4 for x = 6
2.)
8y – 22 for y = 9
3.)
12x 8+
4.)
y + 3z for y = 5 and z = 6 23
y
46
50
for x = 7 and y = 4
86
Although they are closely
related, a Great Dane weighs
about 40 times as much as a
Chihuahua.
An expression for the weight of the
Great Dane could be 40c, where c is the
weight of the Chihuahua.
When solving real-world problems, you will need
to translate words, or verbal expressions, into
algebraic expressions.
Notes
In order to translate a word
phrase into an algebraic
expression, we must first
know some key word
phrases for the basic
operations.
Addition Phrases:
More than
Increase by
Greater than
Add
Total
Plus
Sum
Subtraction Phrases:
Decreased by
Difference between
Take Away
Less
Subtract
Less than*
Subtract from*
Multiplication Phrases:
Product
Times
Multiply
Of
Twice or double
Triple
Notes
Division expressions should
be written using the fraction
bar instead of the traditional
division sign.
c
2
t
5
3
x
Examples: Translate Verbal Phrases into
Expressions.
1. 4 less than quantity 6 times a number n.
6n – 4
2. 3 times the sum of 7 and a number y.
3( 7+y )
3. The difference of 22 and the square of a
number x
22 – x2
Board Drill
Translate it mathematical expression
The product of 8 and
the quantity 6 plus a.
Board Drill
Twice the product
of a and b.
Board Drill
Subtract 8 from b
Board Drill
x less than 10
Board Drill
The difference of x
and y
Board Drill
thrice the difference
of a and b
Seatwork
Write the following verbal phrases into
mathematical expressions.
1.Twice the number b.
2. The product of 9 and the quantity x
plus y.
3. Twice the difference of m and n.
4. The sum of a and 2 divided by x
5. 4 subtracted from the product of 8
and n.
Write Equations and Inequalities
Equation – a mathematical sentence
formed by placing the symbol “ = ”
between two expressions.
Inequality – a mathematical sentence
formed by placing one of the symbols
<, <, or >, > between two expressions.
Key Concept
Symbol
Meaning
=
is equal to
Associated
Word
the same as
<
is less than
fewer than
<
is less than or
equal to
at most
no more than
>
is greater than
more than
>
is greater than or
equal to
at least
no less than
Note: Combining Inequalities.
Sometimes two inequalities
are combined. For example, the
inequalities x > 4 and x < 9 can
be combined to form the
inequality 4 < x < 9, which is read
as “ x is greater than 4 and less
than 9.”
Write the following into mathematical
equations or inequalities.
1. The difference of twice a number
and 8 is 12.
Answer: 2k – 8 = 12
2. The product of 6 and a number n
is at least 24.
Answer: 6n > 24
3. The sum of thrice a number m and
10 is at most 32.
Answer: 3m + 10 < 32
Board Drill
Twice the product
of x any y is equal
to 23
Board Drill
6 the quantity 5
plus x is greater
than or equal to 9.
Board Drill
2 times x minus 5 is
at most 3
Board Drill
7 the quantity x
plus c is at least
245
Board Drill
x is greater than
10 and less than 7
Board Drill
The sum of x and
y is at most 8 and
no more than 9
Seatwork
Translate the verbal phrases into mathematical
equations and inequalities.
6. Twice the product of a and b is equal to 7.
7. 3 the quantity m plus n is greater than 8.
8. 5 the quantity c minus d is at least 4.
9. 7 times the difference of x and y is 23.
10. Thrice the product of x and y is less
than or equal to 5.
Homework
Review for a quiz tomorrow.
a. Evaluate Expressions.
b. Order of Operations
c. Write Expressions, Equations,
and Inequalities.
• Answer page 24 (UBD Book)
Items 2 to 11