Upload
wang-barlow
View
76
Download
0
Embed Size (px)
DESCRIPTION
Section 1.8. Introduction to Variables, Algebraic Expressions, and Equations. A combination of operations on letters (variables) and numbers is called an algebraic expression. Algebraic Expressions 5 + x 6 y 3 y – 4 + x. 4 x means 4 x and xy means x y. - PowerPoint PPT Presentation
Citation preview
Introduction to Variables, Introduction to Variables, Algebraic Expressions, and Algebraic Expressions, and EquationsEquations
Section 1.8
A combination of operations on letters A combination of operations on letters (variables) and numbers is called an (variables) and numbers is called an algebraic algebraic expressionexpression..
Algebraic ExpressionsAlgebraic Expressions
5 + 5 + xx 6 6 yy 3 3 yy – 4 + – 4 + xx
44xx meansmeans 4 4 xx
andand
xyxy meansmeans xx yy
2Martin-Gay, Prealgebra, 5ed
Replacing a variable in an expression Replacing a variable in an expression by a number and then finding the by a number and then finding the value of the expression is called value of the expression is called evaluating the expression evaluating the expression for the for the variable.variable.
3Martin-Gay, Prealgebra, 5ed
Evaluate x + y for x = 5 and y = 2.
Evaluating Algebraic ExpressionsEvaluating Algebraic Expressions
x + y = ( ) + ( )
Replace x with 5 and y with 2 in x + y.
5 2
= 7
4Martin-Gay, Prealgebra, 5ed
EquationEquation
Statements like 5 Statements like 5 ++ 2 2 == 7 are called 7 are called equationsequations..
An equation is of the form An equation is of the form expression expression == expression expression
An equation can be labeled as An equation can be labeled as Equal sign
left side right side
x + 5 = 9
Solving/SolutionSolving/Solution
When an equation contains a variable, When an equation contains a variable, deciding which values of the variable deciding which values of the variable make an equation a true statement is make an equation a true statement is called called solvingsolving an equation for the an equation for the variable.variable.
A A solutionsolution of an equation is a value for of an equation is a value for the variable that makes an equation a the variable that makes an equation a true statement.true statement.
Martin-Gay, Prealgebra, 5ed
Solving/Solution ...Solving/Solution ...
Determine whether a number is a solution: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.
Solving/Solution ...Solving/Solution ...
Determine whether a number is a solution: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.
To solve an equation, we will use To solve an equation, we will use properties of equality to write simpler properties of equality to write simpler equations, all equivalent to the original equations, all equivalent to the original equation, until the final equation has the equation, until the final equation has the form form xx == number number or or number number == xx
Equivalent equationsEquivalent equations have the have the samesame solutionsolution. . The word “number” above represents the The word “number” above represents the solution of the original equation.solution of the original equation.
Solving/Solution...Solving/Solution...
Keywords and phrases suggesting addition, subtraction, multiplication, division or equals.
AdditionAddition SubtractionSubtraction MultiplicationMultiplication DivisionDivision Equal Equal SignSign
sumsum differencedifference productproduct quotientquotient equalsequals
plusplus minusminus timestimes intointo givesgives
added toadded to less thanless than ofof perper isis//waswas// will bewill be
more thanmore than lessless twicetwice dividedivide yieldsyields
totaltotal decreased decreased byby
multiplymultiply divided divided byby
amounts amounts toto
increased increased byby
subtracted subtracted fromfrom
doubledouble is equal is equal toto
10Martin-Gay, Prealgebra, 5ed
the product of 5 and a numberthe product of 5 and a number55xx
twice a numbertwice a number22xx
a number decreased by 3a number decreased by 3nn -- 3 3
a number increased by 2a number increased by 2zz ++ 2 2
four times a numberfour times a number44ww
Translating Word Phrases Translating Word Phrases into Expressionsinto Expressions
11Martin-Gay, Prealgebra, 5ed
x ++ 7 7
three times the sum of a number and 7three times the sum of a number and 7
3(3(x ++ 7) 7)
the quotient of 5 and a numberthe quotient of 5 and a number
the sum of a number and 7the sum of a number and 7
5
x
Additional Word Phrases into Additional Word Phrases into Algebraic Expressions ...Algebraic Expressions ...
12Martin-Gay, Prealgebra, 5ed
Helpful HintHelpful Hint
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
13Martin-Gay, Prealgebra, 5ed