When you're working with equations, knowing the properties of equality is really important. These properties help you change equations while keeping them correct, which makes it easier to find unknown values. Here’s a simple guide to how they work:

1. Addition Property: If you add the same number to both sides of an equation, it stays equal. For example, if you start with $x + 3 = 7$, you can subtract 3 from both sides to find $x$. That gives you $x = 4$.

2. Subtraction Property: Just like addition, if you take away the same number from both sides, the equation stays balanced. So if you have $y - 5 = 10$, and you add 5 to both sides, you get $y = 15$.

3. Multiplication Property: When you multiply both sides by the same number (as long as it’s not zero), the equation is still true. For example, with $2z = 10$, if you divide both sides by 2, you find $z = 5$.

4. Division Property: This is the opposite of multiplication. If you divide both sides of an equation by the same number (again, not zero), it keeps the equation balanced.

By using these properties, you can rearrange equations easily and in a step-by-step way. This really helps make solving linear equations clearer and simpler!