Page 629 - Basic College Mathematics with Early Integers

Chapter 8 Vocabulary Check

Fill in each blank with one of the words or phrases listed below.
variable addition constant algebraic expression equation

terms simplified multiplication evaluating the expression solution
like combined numerical coefficient distributive
1. An algebraic expression is 9. A(n) is of the form
when all like terms have been expression = expression.
. 10. A(n) of an equation is a
2. Terms that are exactly the same, except that they may value for the variable that makes the equation a true
have different numerical coefficients, are called statement.
terms. 11. To multiply -3(2x + 1) , we use the
3. A letter used to represent a number is called a(n) property.
. 12. By the property of
4. A combination of operations on variables and equality, we may multiply or divide both sides of an
numbers is called a(n) . equation by any nonzero number without changing
5. The addends of an algebraic expression are called the the solution of the equation.
of the expression. 13. By the property of equal-
6. The number factor of a variable term is called the ity, the same number may be added to or subtracted
. from both sides of an equation without changing the
solution of the equation.
7. Replacing a variable in an expression by a number
and then finding the value of the expression is called
for the variable.
8. A term that is a number only is called a(n) Are you preparing for your
. test? Don’t forget to take the Chapter 8 Test on
page 614. Then check your answers at the back
of the text and use the Chapter Test Prep
Videos to see the fully worked-out solutions to
8 Chapter Highlights any of the exercises you want to review.

Definitions and Concepts Examples

Section 8.1 Variable Expressions

A letter used to represent a number is called a variable. x, y, z, a, b
A combination of numbers, letters (variables), and operation 3 + x, 7y, x + y - 10
3
symbols is called an algebraic expression, or expression.
Replacing a variable in an expression by a number and Evaluate: 2x + y when x = 22 and y = 4
then finding the value of the expression is called
#
2x + y = 2 22 + 4 Replace x with 22 and y with 4.
evaluating the expression.
= 44 + 4 Multiply.
= 48 Add.
The addends of an algebraic expression are called the 2
terms of the expression. 5x +(–4x)+(–2)
3 terms
The number factor of a variable term is called the Term Numerical Coefficient
numerical coefficient. 7x 7
-6y -6
Terms that are exactly the same, except that they may
x or 1x 1
have different numerical coefficients, are called like 5x + 11x = 15 + 112x = 16x
terms. Copyright 2012 Pearson Education, Inc.
a Q
An algebraic expression is simplified when all like terms like terms
have been combined. b R
y - 6y = 11 - 62y =-5y

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