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Solving Linear Equations definitions

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  • Linear Equation
    An algebraic statement where variable terms and constants are combined using addition, subtraction, multiplication, or division, and the variable has an exponent of one.
  • Variable
    A symbol, often x, representing an unknown value that can be solved for in an equation.
  • Coefficient
    A numerical factor that multiplies a variable in an algebraic expression.
  • Constant
    A fixed value in an equation that does not contain a variable.
  • Like Terms
    Terms in an expression that have identical variable parts and can be combined by addition or subtraction.
  • Distributive Property
    A rule allowing multiplication to be applied across terms inside parentheses, such as a(b + c) = ab + ac.
  • Property of Equality
    A rule stating that performing the same operation on both sides of an equation keeps the equation balanced.
  • Solution Set
    All values for the variable that make the equation a true statement when substituted.
  • Identity
    An equation that is always true for any value of the variable, resulting in infinite solutions.
  • Contradiction
    An equation that is never true, regardless of the variable's value, resulting in no solutions.
  • Conditional Equation
    An equation that is true only for specific values of the variable, resulting in exactly one solution.
  • Least Common Denominator
    The smallest shared multiple of denominators in an equation, used to clear fractions.
  • Set Builder Notation
    A way to describe a set by stating the properties that its members must satisfy, often used for solution sets.
  • Empty Set
    A set containing no elements, representing no solutions to an equation.
  • Multiplication Property of Equality
    A rule stating that multiplying both sides of an equation by the same nonzero number keeps the equation balanced.