Which property states that if you add the same number to both sides of an equation, the equation remains true?

The property that states if you add the same number to both sides of an equation, the equation remains true is known as the Addition Property of Equality. This fundamental concept in algebra ensures that equations maintain their balance when the same value is applied to both sides. For example, if you have an equation such as ( x + 3 = 7 ), adding 2 to both sides results in ( x + 3 + 2 = 7 + 2 ), yielding ( x + 5 = 9 ). This principle is essential for solving equations and it helps students understand that performing the same operation on both sides of an equation does not alter its equality.

The other properties mentioned do not pertain to this specific operation. The Substitution Property relates to replacing a variable with an equivalent expression. The Transitive Property involves comparisons, stating that if one value equals a second value, and that second value equals a third, then the first value equals the third. The Symmetric Property states that if one value is equal to another, then the second is equal to the first. Each property serves a different purpose in mathematics, but for the action of adding the same number to both sides of an equation, the Addition Property of Equality is the