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 Expressions 5 + x 6 y 3 y – 4 + x 4x means 4 x and xy means x y Algebraic Expressions

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 © 2011 Pearson Prentice Hall. All rights reserved 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

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 © 2011 Pearson Prentice Hall. All rights reserved Evaluate x + y for x = 5 and y = 2. x + y = ( ) + ( ) Replace x with 5 and y with 2 in x + y. 52 = 7 Evaluating Algebraic Expressions

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 © 2011 Pearson Prentice Hall. All rights reserved Equation Statements like = 7 are called equations. An equation is of the form expression = expression An equation can be labeled as Equal sign left sideright side x + 5 = 9

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 © 2011 Pearson Prentice Hall. All rights reserved 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.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 © 2011 Pearson Prentice Hall. All rights reserved 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 ? True Since –3 = –3 is a true statement, –2 is a solution of the equation.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88 © 2011 Pearson Prentice Hall. All rights reserved 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 ? False Since 29 = 30 is a false statement, 6 is not a solution of the equation.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99 © 2011 Pearson Prentice Hall. All rights reserved 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.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 10 © 2011 Pearson Prentice Hall. All rights reserved Keywords and phrases suggesting addition, subtraction, multiplication, division or equals. AdditionSubtractionMultiplicationDivisionEqual Sign sumdifferenceproductquotientequals plusminustimesdividegives added tosubtractmultiplyshared equally among is/was/will be more thanless thanmultiply byperyields increased bydecreased byofdivided byamounts to totallessdouble/tripledivided intois equal to Keywords and Phrases

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 11 © 2011 Pearson Prentice Hall. All rights reserved Translating Word Phrases the product of 5 and a number 5x5x twice a number 2x2x a number decreased by 3 n – 3 a number increased by 2 z + 2 four times a number 4w4w

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 12 © 2011 Pearson Prentice Hall. All rights reserved 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 7

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 13 © 2011 Pearson Prentice Hall. All rights reserved Remember that order is important when subtracting. Study the order of numbers and variables below. PhraseTranslation a number decreased by 5 x – 5 a number subtracted from 5 5 – x Helpful Hint