Here are the definitions for the terms you've requested:
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Inverse Operations: Inverse operations are pairs of mathematical operations that reverse the effect of each other. For example, addition and subtraction are inverse operations, as are multiplication and division. When one operation is applied followed by its inverse, the result will be the original number. For instance, if you add 5 to a number and then subtract 5, you return to the original number.
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Linear Equation: A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the power of one. It can be expressed in the standard form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are constants, and \(x\) and \(y\) are variables. The graph of a linear equation is always a straight line.
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Multiplication Property of Equality: The multiplication property of equality states that if two expressions are equal, multiplying both sides of the equation by the same nonzero number will keep the equation balanced. In other words, if \(a = b\), then \(a \cdot c = b \cdot c\) for any \(c \neq 0\).
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Solution: In mathematics, a solution refers to a value or a set of values that satisfy an equation or a system of equations. For example, in the equation \(x + 3 = 5\), the solution is \(x = 2\), since substituting \(2\) for \(x\) makes the equation true. In a broader context, solutions can refer to valid inputs for functions or parameters within mathematical models.
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