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The Addition and Subtraction Properties of Equality definitions

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  • Linear Equation
    An algebraic statement with a variable of degree one and real coefficients, always expressible in the form ax+b=c.
  • Variable
    A symbol, often a letter, representing an unknown value in an equation, which can be isolated to solve the equation.
  • Coefficient
    A real number multiplying a variable in an algebraic expression, determining the variable's rate of change.
  • Constant
    A fixed value in an equation or expression that does not change, often added or subtracted from a variable term.
  • Solution
    A value for the variable that, when substituted, makes the equation a true statement.
  • Solution Set
    A collection of all values that satisfy an equation, typically written inside curly brackets.
  • Equivalent Equations
    Equations that have the same solution, often formed by performing the same operation on both sides.
  • Addition Property of Equality
    A principle stating that adding the same value to both sides of an equation preserves equality.
  • Subtraction Property of Equality
    A principle stating that subtracting the same value from both sides of an equation preserves equality.
  • Balance Scale
    A visual analogy for equations, illustrating that both sides must remain equal when operations are performed.
  • First Degree Equation
    An equation where the variable has an exponent of one, indicating linearity.
  • Opposite Operations
    Pairs of mathematical actions, such as addition and subtraction, used to cancel each other when solving equations.
  • Curly Brackets
    Symbols used to enclose solution sets, indicating all values that solve an equation.
  • Standard Form
    A way of writing linear equations as ax+b=c, with variables and constants clearly separated.
  • Algebraic Expression
    A mathematical phrase containing variables, coefficients, and constants, but lacking an equality sign.