Final answer:
The Symmetry Property of Equality states that performing the same operation on both sides of an equal sign preserves the equality. This fundamental property is central to solving equations and maintaining balance within mathematical expressions.
Step-by-step explanation:
The Symmetry Property of Equality in mathematics is an important concept commonly used in solving equations. This property states that if you have an equation, and you perform the same operation on both sides of the equals sign, the two sides remain equal. This is essential when simplifying expressions or solving equations, as it allows for operations like addition, subtraction, multiplication, and division to be applied uniformly across the equation without altering its truth.
As an example of this property, consider the equation 5 = 5. If you multiply both sides by 2, the equation remains in balance, as 10 = 10. Similarly, if you add 3 to both sides of the original equation, it transforms into 8 = 8, which is still true. Therefore, the Symmetry Property of Equality highlights an important symmetry in the sense that whatever operation you apply to one side, applying it to the other side maintains the equality.