Section 1.8
Introduction to Variables,
Algebraic Expressions, and
Equations
A combination of operations on letters
(variables) and numbers is called an algebraic
expression.
Algebraic Expressions
5+x
6y
3y – 4 + x
4x means 4  x
and
xy means x  y
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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.
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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
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Equation
Statements like 5 + 2 = 7 are called
equations.
An equation is of the form
expression = expression
An equation can be labeled as
Equal sign
x + 5 = 9
left side right side
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
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
?
- 4 + 1 = -3
-3 = -3
True
Since -3 = -3 is a true statement, -2 is a solution of the equation.
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 - 1 = 30
29 = 30
False
Since 29 = 30 is a false statement, 6 is not a solution of the equation.
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.
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
Martin-Gay, Prealgebra, 5ed
is equal
to
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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
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Additional Word Phrases into
Algebraic Expressions ...
the sum of a number and 7
x+7
three times the sum of a number and 7
3(x + 7)
the quotient of 5 and a number
5
x
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Helpful Hint
Remember that order is important
when subtracting. Study the order of
numbers and variables below.
Phrase
a number
decreased by 5
a number
subtracted from 5
Translation
x–5
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5–x
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