1. The problem is to simplify and explain the properties of equality. 2. The properties of equality are fundamental rules that allow us to manipulate equations while keeping them balanced. 3. The main properties include: - **Reflexive Property:** For any value $a$, $a = a$. - **Symmetric Property:** If $a = b$, then $b = a$. - **Transitive Property:** If $a = b$ and $b = c$, then $a = c$. - **Addition Property:** If $a = b$, then $a + c = b + c$ for any $c$. - **Subtraction Property:** If $a = b$, then $a - c = b - c$ for any $c$. - **Multiplication Property:** If $a = b$, then $ac = bc$ for any $c$. - **Division Property:** If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. 4. These properties ensure that performing the same operation on both sides of an equation keeps it true. 5. Conclusion: The properties of equality allow us to solve equations and prove statements by ensuring that equations remain balanced and valid through various algebraic manipulations.