91Ó°ÊÓ

Solving an equation involves finding the value of an unknown variable that makes the equation true. In the given exercise, our goal was to find the value of the variable \( n \) in the equation \( n - 17 = 39 \). This process requires strategic manipulation of the equation to isolate the variable on one side.

We started with the equation \( n - 17 = 39 \) and needed to solve for \( n \). To achieve this, we employed the technique of removing the constant term (\( -17 \)) from the left side. By performing operations that maintain the equation's balance, we can preserve its equality while isolating the variable. Eventually, the process led us to find \( n = 56 \), meaning 56 satisfies the original equation, making the statement true.

Mathematical justification is a crucial part of solving equations. It involves explaining why each step taken during the process is valid and ensures that the overall solution is correct.

In the given problem, we used the Addition Property of Equality, which is our mathematical justification for adding 17 to both sides of the equation. This property confirms that if you add the same number to both sides of an equation, the equation remains balanced and true.

By documenting our steps and reasoning, we ensure that anyone reviewing the solution can follow the logic and understand how we arrived at the solution \( n = 56 \). This not only demonstrates our comprehension of the mathematical principles involved, but also provides confidence in the accuracy of our answer.

Properties of Equality are fundamental rules in mathematics that allow us to manipulate equations in a logical manner. The Addition Property of Equality is one such rule and was pivotal in solving the exercise.

• Addition Property of Equality: This property states that adding the same number to both sides of an equation does not change the equality. If \( a = b \), then \( a + c = b + c \).
• Other Properties: While not used in this particular solution, other properties of equality include the Subtraction, Multiplication, and Division properties. These allow for similar operations in the context of their respective actions.

By using these properties effectively, we maintain the balance of the equation throughout our transformations, ensuring we achieve a correct and justified solution.