Properties of Equality

When solving equations, you need to keep both sides balanced. Properties of equality are the rules that let you do this correctly. Think of an equation as a balanced scale—whatever you do to one side, you must do to the other.

The reflexive property says that any number equals itself $a = a$. The symmetric property means if a = b, then b = a. The transitive property states that if a = b and b = c, then a = c. These foundational properties help us understand how equality works.

When solving equations, you'll use the addition property (adding the same value to both sides) and the subtraction property (subtracting the same value from both sides). The multiplication property and division property work similarly—multiply or divide both sides by the same non-zero number to maintain equality.

💡 Think of these properties as the "rules of the game" for equations. Just like how you need to follow rules in a video game to win, you need to follow these properties to correctly solve algebra problems!

The substitution property is especially useful—it says you can replace any part of an equation with an equal value. For example, if x = 5, you can replace x with 5 in any equation containing x.