A variable is a symbol that represents a number. A variable can represent
any number. In the algebraic expression
27 + *b*
,
*b*
is a variable.
Likewise, variables can appear in equations. In the algebraic
equation
11×*s* = 22
,
*s*
is a variable. If we replace
*s*
with the number
2, the equation will be true, since
11×2 = 22
.

We use variables in algebraic expressions when the quantity of something is
unknown. For example, if I want to talk about "Peter's monthly salary plus
$200," but I do not know his monthly salary, I might write
*s* + 200
, where
*s*
represents Peter's monthly salary in dollars. Or, if I want to say, "My book
weighs three times as much as yours, plus 5 lbs. more," but I do not know how
much your book weighs, I might write that my book weighs
3*w* + 5
, where
*w*
represents the weight of your book in pounds.

We also use variables to represent unknowns in algebraic equations. Consider
the statement, "If Greg grows 2 inches, he will be 60 inches tall." This
statement says that Greg's current height plus 2 inches is equal to 60 inches.
We write
*h* + 2 = 60
, where
*h*
represents Greg's current height.

Algebraic expressions and algebraic equations can contain more than one
variable. For example,
2×(*h* + *w*)
is an algebraic expression that contains two
variables,
*h*
and
*w*
.

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