1 8 Introduction to Variables Algebraic Expressions and

Algebraic Expressions 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 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 2

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. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 3

Evaluating Algebraic Expressions Evaluate x + y for x = 5 and y = 2. Replace x with 5 and y with 2 in x + y = ( ) + ( ) 5 2 = 7 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 4

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 x + 5 = 9 left side right side Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 5

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

Solutions Determine whether a number is a solution: Is – 2 a solution of the equation 2 y + 1 = – 3? Replace y with – 2 in the equation. 2 y + 1 = – 3 ? 2(– 2) + 1 = – 3 ? – 4 + 1 = – 3 True Since – 3 = – 3 is a true statement, – 2 is a solution of the equation. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 7

Solutions Determine whether a number is a solution: Is 6 a solution of the equation 5 x – 1 = 30? Replace x with 6 in the equation. 5 x – 1 = 30 ? 5(6) – 1 = 30 ? 30 – 1 = 30 29 = 30 False Since 29 = 30 is a false statement, 6 is not a solution of the equation. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 8

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. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 9

Keywords and Phrases Keywords and phrases suggesting addition, subtraction, multiplication, division or equals. Addition Subtraction Multiplication Division Equal Sign sum difference product quotient equals plus minus times into gives added to less than of per is/was/ will be more than less twice divide yields total decreased by multiply increased by subtracted from double divided by amounts to is equal to Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 10

Translating Word Phrases the product of 5 and a number 5 x twice a number 2 x a number decreased by 3 n – 3 a number increased by 2 z + 2 four times a number 4 w Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 11

Additional Word Phrases the sum of a number and 7 x + 7 three times the sum of a number and 7 3(x + 7) the quotient of 5 and a number Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 12

Helpful Hint Remember that order is important when subtracting. Study the order of numbers and variables below. Phrase a number decreased by 5 a number subtracted from 5 Translation x – 5 5 – x Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6 ed 13