chapter 1 section 3 copyright © 2008 pearson education, inc. publishing as pearson addison-wesley
TRANSCRIPT
Chapter Chapter 11Section Section 33
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Variables, Expressions, and Equations
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1.31.31.31.3Evaluate algebraic expressions, given values for the variables.Translate word phrases to algebraic expressions.Identify solutions of equations.Identify solutions of equations from a set of numbers.Distinguish between expressions and equations.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Variables, Expressions, and Equations
A variable is a symbol, usually a letter such as x, y, or z, used to represent any unknown number.
5x 2 9m 28 6 2p p In , the 2m means , the product of 2 and m; 8p2
represents the product of 8 and p2. Also, means the product of 6 and .
2 9m 2 m6( 2)p
2p
An algebraic expression is a sequence of numbers, variables operation symbols and/or grouping symbols (such as parentheses) formed according to the rules of algebra.
, , Algebraic expressions
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Objective 11
Evaluate algebraic expressions,
given values for the variables.
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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 1
Find the value of each algebraic expression when .
Evaluating Expressions
Remember, 2p3 means 2 · p3, not 2p· 2p · 2p. Unless parentheses are used, the exponent refers only to the variable or number just before it. To write 2p· 2p · 2p with exponents, use (2p)3.
16 p
32 p
48316
332 2 27 54
3p
Solution:
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EXAMPLE 2
Find the value of each expression when and
.Solution:
Evaluating Expressions
6x 9y
4 5x y
4 2
1
x y
x
2 22x y
94 56
4 26 9
6 1
24 45 69
24 18
7
6
7
2 22 6 9 2 36 81 72 81 153A sequence such as 3) · x ( + y is not an algebraic expression because the rules of algebra require a closing parentheses or bracket for every opening parentheses or bracket
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Objective 22
Translate word phrases to algebraic expressions.
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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 3
Solution:
Using Variables to Write Word Phrases as Algebraic Expressions
Write each word phrase as an algebraic expression using x as the variable.
A number subtracted from 48
The product of 6 and a number
9 multiplied by the sum of a number and 5
48 x
6x
9 5x
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Objective 33
Identify solutions of equations.
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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
An equation is a statement that two algebraic expressions are equal. Therefore, an equation always includes the equality symbol, = .
Identify solutions of equations.
To solve an equation means to find the values of the variable that make the equation true. Such values of the variable are called the solutions of the equation.
4 11x 2 16y 4 1 25p p
2 4z 3 10
4 2x 4 0.5 2m m }Equations
, ,
, ,
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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 4
Solution:
Deciding whether a Number Is a Solution of an Equation
Yes
Decide whether the given number is a solution of the equation.
8 11 5; 2p 8 12 1 5
16 11 5
5 5
Remember that the rules of operations still apply to equations.
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Objective 44
Identify solutions of equations from a set of numbers.
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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
A set is a collection of objects. In mathematics these objects are most often numbers. The objects that belong to the set, called elements of the set, are written between braces. For example, the set containing the numbers (or elements) 1, 2, 3, 4, and 5 is written as
{1, 2, 3, 4, 5}.
One way of determining solutions is the direct substitution of all possible replacements. The ones that lead to true statements are solutions.
Identify solutions of equations from a set of numbers.
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EXAMPLE 5
Solution:
Finding a Solution from a Given Set
Write the statement as an equation. Find all solutions from the set {0, 2, 4, 6, 8, 10}.
Three times a number is subtracted from 21, giving 15.
21 3 15x
2 is the solution from this set of elements.
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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 55
Distinguish between expressions and equations.
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Distinguish between equations and expressions.
An equation is a sentence—it has something on the left side, an = sign, and something on the right side.
4 5 9x 4 5x
Equation
(to solve)
Expression
(to simplify or evaluate)
One way to help figure this out is, equation and equal are similar.
An expression is a phrase that represents a number.
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Decide whether the following is an equation or an
expression.
EXAMPLE 6Distinguishing between Equations and Expressions
Solution:
There is no equals sign, so this
is an expression.
3 1
5
x
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