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A2 - 1.1 Notes

Algebra 2<br>1.1 Notes

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A2 - 1.1 Notes

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  1. 1.1 – Numbers, Expressions, and Equations

  2. Topics • Subsets and Properties of Real Numbers • Evaluating and Simplifying Algebraic Expressions • Solving Linear Equations • Rewriting Formulas and Equations • Problem Solving Strategies and Models • Solving Linear Inequalities • Solving Absolute Value Equations and Inequalities

  3. Subsets of Real Numbers • Natural Numbers: the set of numbers starting at 1 and increasing toward infinity; also called the “counting numbers” • Whole Numbers: the set of numbers starting at 0 and increasing toward infinity; the natural numbers and zero • Integers: the set of whole numbers and their opposites • Rational Numbers: the set of numbers that can be written as a ratio of integers • Irrational Numbers: the set of numbers that cannot be written as a ratio of integers • Real Numbers: the set of numbers, including both rational and irrational numbers, that exist in the real world

  4. Field Properties of Real Numbers

  5. Order of Operations • Parentheses • Exponents • Multiplication • Division • Addition • Subtraction • *a note – if you cannot simplify the operation inside the parentheses, you might need to distribute or apply one of the other field properties to continue simplifying or solving.

  6. Simplifying and Evaluating Expressions • Simplifying means combining all like terms and performing as many operations as possible. 9 + (3x – 2x)3 + 4x – 12 = 9 + 9x – 6x + 4x -12 = 7x – 3 • Evaluating means substituting a certain value for a variable and completing the remaining operations. Evaluate the above example at x = 5: 7x – 3 7(5) – 3 = 35 – 3 = 32

  7. Equality Properties

  8. Solving Linear Equations • The goal of solving linear equations is to get the variable you are solving for alone on one side of the equal sign. • Use the Equality Properties to achieve this. • Example:

  9. Writing Linear Equations Example: During one shift, a waiter earns wages of $20 and gets an additional 15% in tops on customers’ food bills. The waiter earns $105. What is the total of the customers’ food bills? Verbal Model: Income (dollars) = Wages (dollars) + Percent for tips · Food bills (dollars) Equation: 105 = 30 + .15 x Solve the Equation: 75 = .15x x = $500 The total of the customers’ food bills was $500

  10. Rewriting Formulas and Equations • A formula is an equation that relates two or more quantities, usually represented by variables • To solve for a variable means to rewrite an equation as an equivalent equation in which the variable is on one side and does not appear on the other side. Example: Solve for y.

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