Final answer:
Equations are balanced through using properties such as multiplication, division, addition, or subtraction, applied equally to both sides.
Step-by-step explanation:
The question is about solving equations and identifying the properties used in each solution process. When we multiply or divide both sides of an equation by the same number, we use the Multiplication or Division Property of Equality, respectively. This is because these operations maintain the balance of the equation, similar to adding the same amount to both sides (the Addition Property of Equality) and subtracting the same amount from both sides (the Subtraction Property of Equality). For example, if you divide both sides of an equation by the same non-zero number, every term is affected equally, keeping the equation balanced.