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The Addition and Subtraction Properties of Equality definitions

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  • Linear Equation
    A mathematical statement with a variable raised only to the first power, often written as ax + b = c.
  • Variable
    A symbol, often a letter, representing an unknown value that can change within an equation.
  • Coefficient
    A numerical factor multiplied by a variable in an algebraic expression.
  • Constant
    A fixed value in an equation that does not change or contain variables.
  • Solution
    A value for the variable that makes an equation a true statement when substituted.
  • Solution Set
    A collection of all values that satisfy a given equation, typically shown in curly brackets.
  • Addition Property of Equality
    A rule stating that adding the same value to both sides of an equation keeps the equation balanced.
  • Subtraction Property of Equality
    A rule stating that subtracting the same value from both sides of an equation keeps the equation balanced.
  • Equivalent Equations
    Different equations that have the same solution or solution set.
  • First Degree Polynomial
    An algebraic expression where the highest exponent of the variable is one.
  • Expression
    A combination of numbers, variables, and operations without an equal sign.
  • Balance Scale
    A visual analogy used to illustrate that both sides of an equation must remain equal after operations.
  • Standard Form
    A way of writing equations where terms are ordered, typically as ax + b = c for linear equations.
  • Opposite Operations
    Operations that reverse each other's effects, such as addition and subtraction, used to isolate variables.
  • Verification
    The process of checking a proposed solution by substituting it back into the original equation.