Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.8 Introduction to...

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

1.8

Introduction to Variables, Algebraic

Expressions, and Equations

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22

© 2011 Pearson Prentice Hall. All rights reserved

A combination of operations on letters (variables) and numbers is called an algebraic expression.

Algebraic Expressions5 + x 6 •• y 3 •• y – 4 + x

44xx means 4 means 4 •• xxandand

xyxy means means xx •• yy

Algebraic Expressions



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.

Algebraic Expressions



Evaluate x + y for x = 5 and y = 2.

x + y = ( ) + ( )

Replace x with 5 and y with 2 in x + y.

5 2

= 7

Evaluating Algebraic Expressions



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

left side right side

x + 5 = 9



Solutions

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.



Solutions

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

?

TrueTrue

Since –3 = –3 is a true statement, –2 is a solution of the equation.



Solutions

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

?

FalseFalse

Since 29 = 30 is a false statement, 6 is not a solution of the equation.



Solutions

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 divide gives

added to subtract multiply shared equally among

is/was/will be

more than less than multiply by per yields

increased by

decreased by of divided by amounts to

total less double/triple divided into is equal to

Keywords and Phrases



Translating Word Phrases

the product of 5 and a number5x

twice a number2x

a number decreased by 3n – 3

a number increased by 2z + 2

four times a number4w



Additional Word Phrases

x + 7

three times the sum of a number and 7

3(x + 7)

the quotient of 5 and a number

the sum of a number and 7the sum of a number and 7

5

x



Remember that order is important when subtracting. Study the order of numbers and variables below.

Phrase Translation

a number decreased by 5

x – 5

a number subtracted from 5

5 – x

Helpful Hint

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.8 Introduction to...

Documents

Transcript of Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.8 Introduction to...