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Linear Equations definitions

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  • Linear Equation
    A mathematical statement formed by setting a linear expression equal to a value, typically involving one variable.
  • Linear Expression
    A combination of numbers, variables, and operations without an equal sign, such as 2x + 3.
  • Variable
    A symbol, often x, representing an unknown value to be determined in an equation.
  • Constant
    A fixed numerical value in an equation or expression, not multiplied by a variable.
  • Operation
    A mathematical process such as addition, subtraction, multiplication, or division applied to terms.
  • Isolating x
    The process of manipulating an equation to get the variable alone on one side.
  • Opposite Operation
    A mathematical action that reverses another, such as subtraction for addition or division for multiplication.
  • Distributive Property
    A rule allowing multiplication across terms inside parentheses, such as a(b + c) = ab + ac.
  • Like Terms
    Terms in an expression or equation that have the same variable raised to the same power and can be combined.
  • Least Common Denominator
    The smallest shared multiple of denominators in a linear equation with fractions, used to clear fractions.
  • Solution Set
    A collection of all values that satisfy a given equation, often written in set notation.
  • Conditional Equation
    A linear equation that is true for exactly one value of the variable.
  • Identity Equation
    A linear equation that is true for all possible values of the variable, resulting in infinite solutions.
  • Inconsistent Equation
    A linear equation that has no possible solution, often leading to a false statement like 0 = 4.
  • Empty Set
    A solution set containing no elements, indicating that an equation has no solution.