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Math 64 1.8 "Introduction to Variables, Algebraic Expressions, and Equations" Objectives: * Evaluate algebraic expressions given replacement values. * Identify solutions of equations. * Translate phrases into variable expressions. Evaluating Algebraic Expressions Perhaps the most important quality of mathematics is that it is a science of patterns. Communicating about patterns is often made easier by using a letter to represent all the numbers …tting a pattern. We call such a letter a variable. Using variable notation is a primary goal of learning algebra. We now take some important …rst steps in beginning to use variable notation. A combination of operations on letter (variables) and numbers is called an algebraic expression or simply an expression. : Replacing a variable in an expression by a number and then …nding the value of the expression is called evaluating the expression for the variable. When …nding the value of an expression, remember to follow the order of operations. Example 1: (Evaluating algebraic expressions) Evaluate each expression for x = 2; y = 5; and z = 3: a) x5 + (y c) xy (5 + z z) x) b) z d) x + 2y 7x + 2y 3x Identifying Solutions of Equations 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. Page: 1 Notes by Bibiana Lopez Prealgebra by Elayn Martin-Gay 1.8 Example 2: (Identifying solutions of equations) Determine which numbers in each set are solutions to the corresponding equations. a) 3 (n 4) = 10; f5; 7; 10g b) 9x 15 = 5x + 1; f2; 4; 11g Translating Phrases into Variable Expressions To aid us in solving problems later, we practice translating verbal phrases into algebraic expressions. Certain key words and phrases suggesting addition, subtraction, multiplication, or division are reviewed next. Key Words That Indicate Operations: Addition (+) Subtraction ( ) Multiplication ( ) Division ( ) sum di¤erence product quotient plus minus times divide added to subtract multiply shared equally among more than less than multiply by per increased by decreased by of divided by total less double/triple divided into Example 3: (Translating phrases into variable expressions) Write as an algebraic expression. Use x to represent "a number." a) Twice a number. b) 8 increased by a number. c) 6 less than three times a number. d) Seven times the sum of a number and 2. e) 5 divided by a number plus 3. f) The product of a number and 3 increased by 1. Page: 2 Notes by Bibiana Lopez