Mathematical Concepts and Terms

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Equation

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A mathematical statement that asserts the equality of two expressions, typically connected by an equal sign (=).

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Balanced Hanger

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A visual representation used to illustrate equations, where weights on both sides of a hanger are equal, demonstrating the concept of balance in equations.

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Variable

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A symbol, often a letter, used to represent an unknown or arbitrary number in mathematical expressions and equations.

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Solution

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A value or set of values that, when substituted for the variable(s) in an equation, make the equation true.

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Substitution

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The process of replacing a variable in an equation with a specific value to determine the truth of the equation.

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Inverse Operations

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Mathematical operations that undo each other, such as addition and subtraction, or multiplication and division. Applying inverse operations helps in solving equations while maintaining balance.

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Coefficient

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A numerical factor multiplied by a variable in an algebraic expression, indicating how many times the variable is used as a factor.

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Constant

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A fixed value that does not change, often represented by a number without a variable.

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Expression

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A combination of numbers, variables, and mathematical operations (such as addition or multiplication) that represents a value.

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True Equation

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An equation that holds valid when the values of the variable(s) satisfy the relationship expressed, meaning both sides are equal when the solution is substituted.