Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 2.1 – 2.2 Introduction to Variables, Algebraic Expressions, and Equations

Martin-Gay, Prealgebra, 6ed 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Keywords and phrases suggesting addition, subtraction, multiplication, division or equals. AdditionSubtractionMultiplicationDivisionEqual Sign sumdifferenceproductquotientequals plusminustimesintogives added toless thanofperis/was/ will be more thanlesstwicedivideyields totaldecreased bymultiplydivided byamounts to increased bysubtracted from doubleis equal to Keywords and Phrases

Martin-Gay, Prealgebra, 6ed 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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, 6ed 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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