- The given equation is \(\frac{x}{4} - \frac{3}{4} = 16\).
- The equation transforms into \(\frac{x}{4} - \frac{3}{4} + \frac{3}{4} = 16 + \frac{3}{4}\).
- Since \(\frac{3}{4}\) is added to both sides, the Addition Property of Equality is applied.
- The property used is \(\boxed{\text{Addition Property of Equality}}\).
Explanation
- Analyzing the Provided Equation and Step
We are presented with the equation \(\frac{x}{4} - \frac{3}{4} = 16\). The first step in the solving process is explicitly given as \(\frac{x}{4} - \frac{3}{4} + \frac{3}{4} = 16 + \frac{3}{4}\). Our objective is to identify the mathematical property of equality that justifies this step. The Addition Property of Equality states that if \(a = b\), then \(a + c = b + c\) for any real number \(c\). By comparing the original equation to the modified one, we can see that the value \(\frac{3}{4}\) was added to both the left and right sides of the equation.
- Identifying the Applied Property
By examining the transformation \(\frac{x}{4} - \frac{3}{4} = 16 \implies \frac{x}{4} - \frac{3}{4} + \frac{3}{4} = 16 + \frac{3}{4}\), we observe that the term \(\frac{3}{4}\) has been added to both sides of the equality to isolate the variable term \(\frac{x}{4}\). Since the exact same value was added to both sides, this is a direct application of the Addition Property of Equality. This property ensures that the balance of the equation remains unchanged, allowing for further steps in solving for \(x\).
- Conclusion
Based on the analysis of the operation performed, the property applied is the Addition Property of Equality. Therefore, the correct option is the Addition Property of Equality. The final result is \(\boxed{\text{Addition Property of Equality}}\).
Examples
The Addition Property of Equality is a fundamental tool for solving equations in real-life contexts. For example, if you are tracking your bank balance and you receive a deposit of \(\$50\), you must add \(\$50\) to both sides of your financial equation—your current balance and your records—to maintain an accurate account. If your balance was \(B\), and it increased by \(\$50\) (i.e., \(B = \dots\)), the new balance becomes \(B + 50\). Similarly, when balancing chemical equations or architectural dimensions, ensuring that any adjustment applied to one side of an equality is matched on the other is key to maintaining consistency and correctness in your calculations.