Chapter 1: Sets, Operations and Algebraic Language
1.8: Translating Between English and Algebra
Goal: To use algebra to represent or “model” problem situations, you must know how to
translate commonly encountered verbal phrases and sentences into algebraic expressions
and equations.
Translating Algebraic Expressions
When translating an algebraic expression into a verbal phrase, pay attention to the
arithmetic operation that connects the variable to one or more numbers.
n 5
Represents the sum of n and 5, or equivalently, 5 more than n
n 3
Represents 3 subtracted from n, 3 less than n, or n diminished by 3
n
2
4n  1
2n  3  1
Represents n divided by 2 or one-half of n
Represents 4 times n increased by 1 or, equivalently, 1 more than the
product of 4 and n.
Represents 2 times the sum of n and 3 increased by 1
Tim’s weight exceeds Sue’s weight by 13 If Sue weighs x pounds, then Tim weighs
pounds.
x+13 pounds.
If Time weighs x pounds, then Sue weighs x13 pounds.
The number of dimes exceeds 3 times the If there are x pennies, then there are 3x+2
number of pennies by 2.
dimes
Bill has 7 fewer dollars in his wallet then If there are x pennies, then there are
three times the number Roger has in his
3x  7 dimes
wallet.
The sum of two numbers is 54.
If x represents one of these numbers then 54x represents the other number.
Victor is twice John’s age 8 years ago.
If y is John’s current age, then y-8 represents
John’s age 8 years ago so Victor’s current
age is 2(y-8)
Chapter 1, Section 1.6
Page 1
Chapter 1: Sets, Operations and Algebraic Language
1.8: Translating Between English and Algebra
Translating Verbal Sentence
An inequality is a mathematical statement that two quantities are not equal, as in
2x  1  7 e into an equation or an inequality, identify key phrases that can be translated
directly into mathematical terms.
Two times a number n
increased by 5 is 17
Five times a number n
exceeds 2 times that number
by 21
When 2 is subtracted from a
number n the result is at
most 5
When twice a number x is
increased by 5, the result is
at least 27.
Chapter 1, Section 1.6
Page 2
2n+5=17
5n=2n+21
n25
2x  5  27