1. Introduction to Variables, Algebraic Expressions, and Equations
Chapter 1 / Whole Numbers and Introduction to Algebra
Section 1.8
Introduction to Variables, Algebraic Expressions, and Equations

2. Chapter 1 / Whole Numbers and Introduction to Algebra
A combination of operations on letters (variables) and numbers is called an algebraic expression.
Algebraic Expressions
5 + x  y  y – 4 + x
4x means 4  x
and
xy means x  y
Martin-Gay, Prealgebra, 5ed

3. Chapter 1 / Whole Numbers and Introduction to Algebra
Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating the expression for the variable.
Martin-Gay, Prealgebra, 5ed

4. Chapter 1 / Whole Numbers and Introduction to Algebra
Evaluating Algebraic Expressions
Evaluate x + y for x = 5 and y = 2.
Replace x with 5 and y with 2 in x + y.
x + y = ( ) + ( ) 5 2
= 7
Martin-Gay, Prealgebra, 5ed

5. Chapter 1 / Whole Numbers and Introduction to Algebra
Equation
Statements like = 7 are called equations.
An equation is of the form expression = expression
An equation can be labeled as
Equal sign
x = 9
left side
right side

6. Chapter 1 / Whole Numbers and Introduction to Algebra
Solving/Solution
When an equation contains a variable, deciding which values of the variable make an equation a true statement is called solving an equation for the variable.
A solution of an equation is a value for the variable that makes an equation a true statement.
Martin-Gay, Prealgebra, 5ed

7. Chapter 1 / Whole Numbers and Introduction to Algebra
Solving/Solution ...
Determine whether a number is a solution:
Is -2 a solution of the equation 2y + 1 = -3?
Replace y with -2 in the equation.
2y + 1 = -3 ?
2(-2) + 1 = -3 ?
= -3
-3 = -3
True
Since -3 = -3 is a true statement, -2 is a solution of the equation.

8. Chapter 1 / Whole Numbers and Introduction to Algebra
Solving/Solution ...
Determine whether a number is a solution:
Is 6 a solution of the equation 5x - 1 = 30?
Replace x with 6 in the equation.
5x - 1 = 30 ?
5(6) - 1 = 30 ?
= 30
29 = 30
False
Since 29 = 30 is a false statement, 6 is not a solution of the equation.

9. Chapter 1 / Whole Numbers and Introduction to Algebra
Solving/Solution...
To solve an equation, we will use properties of equality to write simpler equations, all equivalent to the original equation, until the final equation has the form
x = number or number = x
Equivalent equations have the same solution.
The word “number” above represents the solution of the original equation.

10. Chapter 1 / Whole Numbers and Introduction to Algebra
Keywords and phrases suggesting addition, subtraction, multiplication, division or equals.
Addition
Subtraction
Multiplication
Division
Equal Sign
sum
difference
product
quotient
equals
plus
minus
times
into
gives
added to
less than of
per
is/was/ will be
more than
less
twice
divide
yields
total
decreased by
multiply
divided by
amounts to
increased by
subtracted from
double
is equal to
Martin-Gay, Prealgebra, 5ed

11. Chapter 1 / Whole Numbers and Introduction to Algebra
Translating Word Phrases into Expressions
the product of 5 and a number 5x
twice a number 2x
a number decreased by 3
n - 3
a number increased by 2
z + 2
four times a number 4w
Martin-Gay, Prealgebra, 5ed

12. Chapter 1 / Whole Numbers and Introduction to Algebra
Additional Word Phrases into Algebraic Expressions ...
x + 7
three times the sum of a number and 7
3(x + 7)
the quotient of 5 and a number
the sum of a number and 7
Martin-Gay, Prealgebra, 5ed

13. Martin-Gay, Prealgebra, 5ed
Helpful Hint
Remember that order is important when subtracting. Study the order of numbers and variables below.
Phrase
Translation
a number
decreased by 5
x – 5
subtracted from 5
5 – x
Martin-Gay, Prealgebra, 5ed