3: Solving Equations
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- 3.1: The Language of Algebra
- In algebra, we use letters of the alphabet to represent variables. The letters most commonly used for variables are x,y,a,b, and c .
- 3.2: Solving Equations with Addition and Subtraction Properties of Equality
- This page outlines learning objectives for solving equations, emphasizing the use of the Addition and Subtraction Properties of Equality, verifying solutions, and translating words into algebraic expressions. It includes examples and exercises for isolating variables, simplifying before solving, and checking answers. A step-by-step approach to translating word problems into equations is detailed, with practical examples provided.
- 3.3: Solving Equations with the Division and Multiplication Properties of Equality
- This page provides learning objectives and methods for solving equations using the Division and Multiplication Properties of Equality. It includes examples and exercises for isolating variables and solving word problems, emphasizing the importance of defining variables and translating verbal statements into equations.
- 3.4: Solving Equations with Variables and Constants on Both Sides
- In all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we will learn to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.
- 3.5: General Strategy to Solve Linear Equations
- This page provides a comprehensive guide to solving linear equations, outlining a systematic approach that includes simplifying equations, applying the distributive property, collecting like terms, isolating variables, and checking solutions for accuracy. It also categorizes different types of equations—conditional, identities, and contradictions—with definitions and examples, alongside exercises for classification and practice in solving and verifying these equations.
- 3.6: Solving Equations with Fractions or Decimals
- This page presents methods for solving linear equations with fractional and decimal coefficients. It emphasizes strategies for isolating variables, using the least common denominator (LCD) to eliminate fractions, and provides step-by-step exercises to enhance understanding. The content includes summaries of results for various equations, showcasing the final values of multiple variables.
- 3.7: Solving a Formula for a Specific Variable
- This page explains the Distance, Rate, and Time formula d = rt for calculating distance based on constant speed, guiding users through problem-solving processes including variable identification and formula manipulation. It also covers exercises for isolating variables in algebraic formulas like area and simple interest, tackling equations with variables on both sides, and translating word problems into algebraic form.