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Appendix A Definitions

1 Basic Algebraic Presentation

Definition 1.1 Axioms of Equality

2 Variables in Expressions and Equations

Definition 2.1 Variable

3 Like and Unlike Terms

Definition 3.1 Monomial, Coefficient, Variable Part

Definition 3.2 Polynomial

Definition 3.3 Like and Unlike Terms

Definition 3.4 The Distributive Property

Definition 3.5 The Commutative and Associative Properties of Addition

4 Simplifying Expressions and Solving Equations

Definition 4.1 Expression

Definition 4.2 Simplify

Definition 4.3 Equation

Definition 4.4 Solve and Solution of an Equation

Definition 4.5 Inequality

Definition 4.6 Axioms of Inequality

Definition 4.7 Solve and Solution of an Inequality

6 Exponents

Definition 6.1 Exponent

Definition 6.3 Exponent Notation

Definition 6.5 The \(n\)-th root

Definition 6.6 Fractional Exponents

7 Products of Polynomials

Definition 7.1 The Commutative and Associative Properties of Multiplication

8 Common Factors

Definition 8.1 Common Factor

9 Factoring Quadratic Polynomials

Definition 9.1 Monic and Non-Monic Quadratic Polynomials

12 Lines and the Coordinate Plane

Definition 12.1 Linear Equation

Definition 12.2 Function

13 Slope-Intercept Form

Definition 13.1 Slope

Definition 13.2 Slope-Intercept Form

14 Point-Slope Form

Definition 14.1 Point-Slope Form

15 The Method of Substitution

Definition 15.1 System of Simultaneous Linear Equations

17 Fraction Basics

Definition 17.1 Fractions

Definition 17.2 Equivalent Fractions

20 Fraction Division

Definition 20.1 The Reciprocal of a Fraction

24 Rethinking Arithmetic

Definition 24.1 Greater Than and Less Than

27 Negatives on the Number Line

Definition 27.1 Absolute Value

Definition 27.2 Absolute Value

34 Scientific Notation

Definition 34.1 Scientific Notation