§ 1.4 Introduction to Variable Expressions and Equations.

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§ 1.4 Introduction to Variable Expressions and Equations

Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Exponential notation is used to write repeated multiplication in a more compact form. exponent 3434 base The expression 3 4 is called an exponential expression. Exponents Example: Evaluate 2 6.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 33 Order of Operations Simplify expressions using the order below. If grouping symbols such as parentheses are present, simplify expressions within those first, starting with the innermost set. If fraction bars are present, simplify the numerator and the denominator separately. 1. Evaluate exponential expressions 2. Perform multiplication or division in order from left to right. 3. Perform addition or subtraction in order from left to right.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 44 Using the Order of Operations Simplify the expression. Simplify numerator and denominator separately Divide. Add. Simplify. Example:

Martin-Gay, Beginning and Intermediate Algebra, 4ed 55 DefinitionExample Variable: A symbol used to represent a number. Evaluate: 7 + 3z when z = – 3 Algebraic Expression: A collection of numbers, variables, operation symbols, and grouping symbols. Evaluating an Algebraic Expression: Finding its numerical value once we know the values of the variables. Evaluating Algebraic Expressions

Martin-Gay, Beginning and Intermediate Algebra, 4ed 66 Determining Whether a Number is a Solution DefinitionExample Equation: A mathematical statement that two expressions have equal value. 5x = y = 2y – 5 Solving: In an equation containing a variable, finding which values of the variable make the equation a true statement. Solve the equation for a. x + 2 = 16 x = 14 Solution: In an equation, a value for the variable that makes the equation a true statement. Is –7 a solution of: a + 23 = –16? – 7 is not a solution.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 77 Translating Phrases Addition (+) Subtraction (–) Multiplication (·) Division (  ) Equality (=) Sum Plus Added to More than Increased by Total Difference Minus Subtract Less than Decreased by Less Product Times Multiply Twice Of Quotient Divide Into Ratio Divided by Equals Gives Is/was/should be Yields Amounts to Represents

Martin-Gay, Beginning and Intermediate Algebra, 4ed 88 Translating Phrases Write as an algebraic expression. Let x to represent the unknown number. a.) 5 decreased by a number b.) The quotient of a number and 12 5 Translate: 5 decreased bya number – x In words:a.) a number Translate: x and12  In words:b.) The quotient of Example: