Introduction to Variables, Algebraic Expressions, and Equations Chapter 1 / Whole Numbers and Introduction to Algebra Section 1.8 Introduction to Variables, Algebraic Expressions, and Equations

Chapter 1 / Whole Numbers and Introduction to Algebra 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 Martin-Gay, Prealgebra, 5ed

Chapter 1 / Whole Numbers and Introduction to Algebra 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. Martin-Gay, Prealgebra, 5ed

Chapter 1 / Whole Numbers and Introduction to Algebra Evaluating Algebraic Expressions Evaluate x + y for x = 5 and y = 2. Replace x with 5 and y with 2 in x + y. x + y = ( ) + ( ) 5 2 = 7 Martin-Gay, Prealgebra, 5ed

Chapter 1 / Whole Numbers and Introduction to Algebra 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

Chapter 1 / Whole Numbers and Introduction to Algebra Solving/Solution 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, 5ed

Chapter 1 / Whole Numbers and Introduction to Algebra Solving/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 True Since -3 = -3 is a true statement, -2 is a solution of the equation.

Chapter 1 / Whole Numbers and Introduction to Algebra Solving/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 False Since 29 = 30 is a false statement, 6 is not a solution of the equation.

Chapter 1 / Whole Numbers and Introduction to Algebra Solving/Solution... 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.

Chapter 1 / Whole Numbers and Introduction to Algebra 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 divided by amounts to increased by subtracted from double is equal to Martin-Gay, Prealgebra, 5ed

Chapter 1 / Whole Numbers and Introduction to Algebra Translating Word Phrases into Expressions the product of 5 and a number 5x twice a number 2x a number decreased by 3 n - 3 a number increased by 2 z + 2 four times a number 4w Martin-Gay, Prealgebra, 5ed

Chapter 1 / Whole Numbers and Introduction to Algebra Additional Word Phrases into Algebraic Expressions ... 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, 5ed

Martin-Gay, Prealgebra, 5ed Helpful 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 subtracted from 5 5 – x Martin-Gay, Prealgebra, 5ed