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Mastering Equations and Equalities: A Beginner's Guide

In this chapter, you'll discover essential mathematical concepts including the order of operations, number classification, and solving equations involving absolute values. We will unpack the fundamental vocabulary necessary for understanding algebra, including variables, algebraic expressions, and various types of numbers such as real, rational, integers, and irrational numbers. By the end, you'll feel confident solving and graphing equations, making equalities your best friends in math!

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Mastering Equations and Equalities: A Beginner's Guide

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  1. Chapter 1 – Equations and Equalities! In this chapter, order of operations, classifying of numbers, solving equation involving absolute values and lastly equalities will become your best friends  By: Ana Carrazco, JC Nely Jaimes, Kaleen Smith, and Kimberly Gomes

  2. Vocabulary!! • Variables- a letter that represents an unknown quantity • Order of Operations- P E M D A S • Algebraic expression- a combination of numbers, variables, and operations without an equal sign

  3. Vocabulary!! • Real numbers- any number that can be placed on a number line • Rational numbers- a number that can be written as a fraction • Integers - …-2, -1, 0, 1, 2… • Whole numbers– start from zero and up • Natural numbers- start from one and up • Irrational numbers- a number that can’t be written as a fraction • Absolute Value- distance from zero

  4. Properties of real numbers

  5. Note card continued.. P- parenthesis E- exponents M- multiplication D- division A- addition S- subtraction Greater than: greater than or equal to. Less than: less than or equal to. *On a number line, if the symbol is greater than/less than or equal too, fill in the circle on the number line. If the sign is just greater than or equal, leave the circle open.

  6. SAMPLE PROBLEMS SOLVE THEN GRAPH SOLVE WHEN x = 2 3 4 5

  7. Sample problems continued SIMPLIFY EVALUATE THE EXPRESSION WHEN a = 4 b = 6 & c = 10

  8. SAMPLE PROBLEMS CONTINUED Q = Ba 9y + 4 = 85 B B 4 4 Q 9y = 81 B y = 9 SOLVE FOR a SOLVE EQUATION a

  9. SAMPLE PROBLEMS CONTINUED SOLVE THEN GRAPH 6v + 6 ≤ 36 6v + 6 ≥ -36 6 6 6 6 6v ≤ 30 6v ≥ -42 v ≤ 5 v ≥ -7 -7 -5 -3 0 3 5 7

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