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  • RWM102: Algebra
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  • The Subtraction and Addition Properties of Equality
    COURSE INTRODUCTION
    Course Syllabus
    Unit 1: Variables and Variable Expressions
    1.1: Variables, Constants, and Coefficients
    Identifying Variable Parts and Coefficients of Terms
    1.2: Replacing Variables with Their Values
    How to Write Multiplication in Algebra
    Practice Evaluating Expressions in One Variable
    Practice Evaluating Expressions in Two Variables
    1.3: Order of Operations Review
    Order of Operations
    Practice Using PEMDAS
    1.4: Commutative Property of Addition and Multiplication
    Commutative Laws of Addition and Multiplication
    1.5: Associative Property of Addition and Multiplication
    Associative Laws of Addition and Multiplication
    1.6: Distributive Property of Multiplication over Addition/Subtraction
    Distributive Property of Multiplication over Addition
    1.7: Definition and Examples of Like Terms
    Like Terms
    1.8: Simplifying Expressions by Combining Like Terms
    Combining Like Terms
    Practice Combining Like Terms with Negative Coefficients
    Practice Combining Like Terms with Negative Coefficients and Distribution
    Unit 2: Linear Equations
    2.1: Definition of an Equation and a Solution of an Equation
    Solving Linear Equations with One Variable
    2.2: Addition/Subtraction Property of Equations
    The Subtraction and Addition Properties of Equality
    2.3: Multiplication/Division Property of Equations
    The Division and Multiplication Properties of Equality
    2.4: Equations of the Form x + a = b and x − a = b
    Adding and Subtracting the Same Thing to Both Sides
    Practice Solving One-Step Equations
    2.5: Equations of the Form ax = b and x/a = b
    Algebraic Equations with Multiplication and Division
    Practice One-Step Equations with Multiplication and Division
    2.6: Equations of the Form ax + b = c
    Solving More Complicated Equations
    Practice Solving Two-Step Equations
    2.7: Equations of the Form ax + b = cx + d
    Equations with Variables on Both Sides
    Practice Solving Equations with Variables on Both Sides
    2.8: Equations with Parentheses
    Solving Equations with the Distributive Property
    Practice Solving Multistep Equations with Distribution
    2.9: Solving Literal Equation for One of the Variables
    Solving Linear Equations with One Variable
    Solving for One Variable
    Unit 3: Word Problems
    3.1: Mathematical Symbols and Expressions for Common Words and Phrases
    Translating Words into Mathematical Symbols
    3.2: Translating Verbal Expression into Mathematical Equations
    Writing Algebraic Equations
    3.3: Number Problems
    Solving Algebraic Expressions and Equations Part I
    3.4: Consecutive Integer Problems
    Adding Consecutive and Odd Integers
    Solving Algebraic Expressions and Equations Part II
    3.5: General Statement Problems
    Solving Linear Word Problems with Substitution
    Simple Word Problems Resulting In Linear Equations
    3.6: Applying the Uniform Motion Equation
    Solving a Formula for a Specific Variable
    3.7: Value Mixture Problems
    Mixture Problems
    Solving Mixture Word Problems
    Practice Solving Mixture Word Problems
    Solving Percent Word Problems
    Practice Solving Percent Word Problems
    Unit 4: Inequalities
    4.1: Definition and Notation of an Inequality
    Using the Language of Algebra
    4.2: Graphing Inequalities on a Number Line
    Plotting Inequalities on a Number Line
    Introduction to Linear Inequalities
    4.3: Solving One-Step Inequalities
    One-Step Inequalities
    One-Step Inequalities Word Problems
    Practice Solving One-Step Inequalities
    4.4: Solving Multi-Step Inequalities
    Multi-step Inequalities with Variables on Both Sides
    Practice Solving Multipstep Inequalities
    Unit 5: Graphs of Linear Equations and Inequalities
    5.1: Graphing Points in the Rectangular Coordinate Plane
    Points in the Coordinate Plane
    5.2: Ordered Pairs as Solutions of an Equation in Two Variables
    Ordered Pair Solutions to Equations
    Practice Ordered Pair Solutions to Linear Equations
    5.3: Graphing Equations in Two Variables of the Form Ax + By = C
    Graphing Linear Equations with Two Variables
    5.4: Intercepts of a Straight Line
    Graphs with Intercepts
    5.5: Definition of Slope and Slope Formula
    Understanding the Slope of a Line
    5.6: Slopes of Parallel and Perpendicular Lines
    Parallel and Perpendicular Lines
    5.7: Graphing Equations in Two Variables of the Form y = mx + b
    Using the Slope-Intercept Form of an Equation of a Line
    5.8: Point-Slope Form
    Linear Equations in Point-Slope Form
    5.9: Graphing Linear Inequality of Two Variables on the Coordinate Plane
    Graphs of Linear Inequalities
    Unit 6: Systems of Linear Equations and Inequalities
    6.1: Solution of a System of Linear Equations
    Checking Solutions for Systems of Linear Equations
    6.2: Solving Systems of Linear Equations by Graphing
    Using Graphs to Solve Linear Equations
    6.3: Solving Systems of Linear Equations Using the Substitution Method
    Using the Substitution Method
    Practice Using the Substitution Method
    6.4: Solving Systems of Linear Equations Using the Elimination Method
    The Elimination Method
    Practice Solving Linear Equations with Elimination
    6.5: Choosing a Strategy for Solving Systems of Linear Equations
    Comparing Methods for Solving Linear Systems
    6.6: Solving Word Problems by Using Systems of Equations
    Coin and Mixture Problems
    Solving Word Problems with Linear Systems
    Solving Word Problems with Linear Systems
    6.7: Graphing Systems of Linear Inequalities
    Graphing Systems of Linear Inequalities
    6.8: Applications of Systems of Linear Inequalities
    Solving Applications of Linear Inequalities
    Linear Programming
    Unit 7: Operations with Monomials
    7.1: Algebraic Exponential Expressions
    Exponential Expressions
    7.2: Manipulating Exponents
    Exponential Properties Involving Products
    7.3: Quotient of Exponents and Power of a Quotient
    Exponential Properties Involving Quotients
    7.4: Negative Exponents
    Negative Exponent Intuition
    Practice Solving Problems with Negative Exponents
    7.5: Multiplying Monomials
    Multiplication Properties of Exponents
    7.6: Dividing Monomials
    Dividing Monomials
    Unit 8: Operations with Polynomials
    8.1: Classifying Polynomials
    Introduction to Polynomials
    8.2: Adding and Subtracting Polynomials
    Adding and Subtracting Polynomials
    More on Adding and Subtracting Polynomials
    8.3: Multiplying a Polynomial by a Monomial
    Multiplying Monomials by Polynomials
    8.4: Multiplying Binomials (FOIL)
    Using the FOIL Technique to Multiply Binomials
    Multiplying Binomials by a Binomial
    8.5: Complete the Square and Difference of Two Squares
    Finding the Square of a Binomial with One Variable
    Special Products of Polynomials
    8.6: Multiplying Polynomials with Any Number of Terms
    Multiplying a Polynomial by a Binomial
    Multiplying Polynomials
    8.7: Dividing a Polynomial by a Monomial
    Dividing Polynomials with Monomials with Remainder
    Dividing Polynomials
    8.8: Dividing a Polynomial by a Binomial
    Dividing Polynomials by Binomials
    Dividing Polynomials by Binomials
    Unit 9: Factoring Polynomials
    9.1: Identifying Greatest Common Factor
    The Language of Factoring
    Using the Greatest Common Factor and Factoring by Grouping
    9.2: Factoring Polynomials by Grouping
    Factor by Grouping
    Practice Factoring Polynomials
    9.3: Revisiting FOIL by Working Backwards
    Basic Concepts Involved in Factoring Trinomials
    9.4: Factoring Trinomials of the Form x² + bx + c when c is Positive
    Factoring Trinomials
    Practice Factoring Polynomials
    9.5: Factoring Trinomials of the Form x² + bx + c when c is Negative
    Factoring Trinomials of the Form x² + bx + c when c is Negative
    9.6: Factoring by Grouping
    Factoring by Grouping
    Practice Factoring by Grouping
    9.7: Factoring Trinomials of the Form x² + bxy + cy² and ax² + bxy + cy²
    Factoring Trinomials with Two Variables
    Practice Factoring Trinomials with Two Variables
    9.8: Identifying and Factoring Complete Square Trinomials
    Factoring Using Perfect Square Trinomials
    Factoring Perfect Square Trinomials
    9.9: Identifying and Factoring the Difference of Two Squares
    Factoring Using Difference of Squares
    9.10: Identifying and Factoring the Sum and Difference of Two Cubes
    Factoring Sum of Cubes
    9.11: Factoring General Polynomials
    Factoring Polynomials
    More on Factoring Polynomials
    Practice Factoring Polynomials
    9.12: The Principle of Zero Product and Identifying Solutions
    Using the Principle of Zero Product to Solve Quadratic Equations
    9.13: Using Factoring to Solve Quadratic Equations
    Using Factoring to Solve Quadratic Equations
    Using Factoring to Solve Complicated Quadratic Equations
    9.14: Applications for Solving Problems
    Using Factoring to Solve Problems
    Study Guide
    RWM102 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    RWM102: Certificate Final Exam
    Archived Materials
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  1. RWM102: Algebra
  2. Unit 2: Linear Equations
  3. 2.2: Addition/Subtraction Property of Equations
  4. The Subtraction and Addition Properties of Equality

The Subtraction and Addition Properties of Equality

Completion requirements

Read up to the "Solve Equations that Require Simplification" section. Pay attention to the "Solve Equations Using the Subtraction and Addition Properties of Equality" section, which gives a good example of how the two sides of an equation must be equal. After you read, complete examples 2.2 through 2.5 and check your answers.

Click on The Subtraction and Addition Properties of Equality to open the resource.
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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.