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Multiplication Property of Equality
The Multiplication Property of Equality states that multiplying both sides of an equation by the same number preserves the equality. For any numbers , , and :
If , then
This property is used to solve equations in which the variable is divided by a number or has a fractional coefficient. Multiplying both sides by the appropriate value "undoes" the division or fraction. For example, to solve , multiply both sides by to obtain . Similarly, when the coefficient is a fraction such as , multiplying both sides by the reciprocal isolates the variable: . This technique leverages the inverse property of multiplication, since a number multiplied by its reciprocal equals .
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Elementary Algebra @ OpenStax
Ch.3 Math Models - Elementary Algebra @ OpenStax
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Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
Ch.8 Rational Expressions and Equations - Elementary Algebra @ OpenStax
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