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9.1 – Symbols and Sets of Numbers Definitions: Natural Numbers: {1, 2, 3, 4, …} Whole Numbers: All natural numbers plus zero, {0, 1, 2, 3, …} Equality Symbols

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Inequality Symbols 9.1 – Symbols and Sets of Numbers

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Equality and Inequality Symbols are used to create mathematical statements. 9.1 – Symbols and Sets of Numbers

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Order Property for Real Numbers For any two real numbers, a and b, a is less than b if a is to the left of b on the number line – Symbols and Sets of Numbers

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True or False 9.1 – Symbols and Sets of Numbers

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Translating Sentences into Mathematical Statements Fourteen is greater than or equal to fourteen. Zero is less than five. Nine is not equal to ten. The opposite of five is less than or equal to negative two. 9.1 – Symbols and Sets of Numbers

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Identifying Common Sets of Numbers Definitions: 9.1 – Symbols and Sets of Numbers Integers: All positive numbers, negative numbers and zero without fractions and decimals. {…, -3, -2, -1, 0, 1, 2, 3, 4, …}

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Identifying Common Sets of Numbers Definitions: 9.1 – Symbols and Sets of Numbers Rational Numbers: Any number that can be expressed as a quotient of two integers. Irrational Numbers: Any number that can not be expressed as a quotient of two integers.

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Real Numbers IrrationalRational Non-integer rational #s Integers Negative numbers Whole numbers Zero Natural numbers 9.1 – Symbols and Sets of Numbers

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Given the following set of numbers, identify which elements belong in each classification: Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers All elements 9.1 – Symbols and Sets of Numbers

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9.2 – Properties of Real Numbers Commutative Properties Addition: Multiplication:

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Associative Properties Addition: Multiplication: 9.2 – Properties of Real Numbers

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Distributive Property of Multiplication 9.2 – Properties of Real Numbers

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Identity Properties: Addition: Multiplication: 9.2 – Properties of Real Numbers 0 is the identity element for addition 1 is the identity element for multiplication

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Additive Inverse Property: The numbers a and –a are additive inverses or opposites of each other if their sum is zero. Multiplicative Inverse Property: The numbers are reciprocals or multiplicative inverses of each other if their product is one. 9.2 – Properties of Real Numbers

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Name the appropriate property for the given statements: Distributive Commutative prop. of addition Associative property of multiplication Commutative prop. of addition Multiplicative inverse Commutative and associative prop. of multiplication 9.2 – Properties of Real Numbers

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Suggestions for Solving Linear Equations: 1. If fractions exist, multiply by the LCD to clear all fractions. 2. If parentheses exist, used the distributive property to remove them. 3. Simplify each side of the equation by combining like-terms. 4. Get the variable of interest to one side of the equation and all terms to the other side. 5. Use the appropriate properties to get the variable’s coefficient to be Check the solution by substituting it into the original equation. 9.3 – Solving Linear Equations

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Example 1: Check: 9.3 – Solving Linear Equations

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Example 2: Check: 9.3 – Solving Linear Equations

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Example 3: Check: LCD = – Solving Linear Equations

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Example 4: 9.3 – Solving Linear Equations

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Example 4: Check: 9.3 – Solving Linear Equations

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Example 5: Identity Equation – It has an infinite number of solutions. 9.3 – Solving Linear Equations

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Example 6: No Solution LCD = – Solving Linear Equations

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