Page 582 - Basic College Mathematics with Early Integers

8.1 VARIABLE EXPRESSIONS Objectives

Evaluate Algebraic Expressions for
Given Replacement Values for the
Objective Evaluating Algebraic Expressions
Variables.
Recall from Section 2.1 that a combination of numbers, letters (variables), and oper- Use Properties of Numbers
ation symbols is called an algebraic expression or simply an expression. For example,
to Combine Like Terms.
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3 + x, 5 y, and 2 z - 1 + x
Use Properties of Numbers
are expressions. to Multiply Expressions.
If two variables or a number and a variable are next to each other, with no
operation sign between them, the indicated operation is multiplication. For example, Simplify Expressions by
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2x means 2 x Multiplying and Then Combining
Like Terms.
and
Find the Perimeter and Area
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xy or x1y2 means x y
of Figures.
Also, the meaning of an exponent remains the same when the base is a variable. For
example,
x = x x and y 5 = y y y y y
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2
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r
u
2 factors of x 5 factors of y
Throughout this text, we have practiced replacing a variable in an expression by
a number and then finding the value of the expression. Remember that this is called
evaluating the expression. Let’s review this process. When finding the value of an
expression, don’t forget to follow the order of operations.

Example 1 Evaluate: 2x + y when x = 8 and y =-7 PRACTICE 1
Evaluate: 5x - y when x = 2
Solution: Replace x with 8 and y with -7 in 2x + y. and y =-3
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2x + y = 2 8 + 1-72 Replace x with 8 and y with -7.
= 16 + 1-72 Multiply first because of the order of operations.
= 9 Add.
Work Practice 1

3m - 2n
Example 2 Evaluate: when m = 8, n = 4, and q = 1 PRACTICE 2
-2q
5r - 2s
Evaluate: when
Solution: -3q
r = 3, s = 3, and q = 1
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3m - 2n 3 8 - 2 4
= Replace m with 8, n with 4, and q with 1.
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-2q -2 1
24 - 8
= Multiply.
-2
16
= Subtract in the numerator.
-2
=-8 Divide.
Work Practice 2
Answers
1. 13 2. -3
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