- Start with the equation \(d + 10 = 829\).
- Subtract \(10\) from both sides to isolate \(d\).
- Calculate the result: \(829 - 10 = 819\).
- The solution is \(\boxed{819}\).
Explanation
- Analyzing the Equation and Strategy
The goal is to determine the value of \(d\) in the linear equation \(d + 10 = 829\). This is a simple algebraic equation where we need to isolate the variable \(d\). To do this, we can subtract the constant term, \(10\), from both sides of the equation. This operation maintains the balance of the equation while leaving the variable \(d\) by itself on one side.
- Isolating the Variable and Solving
Starting with the given equation \(d + 10 = 829\), we perform the subtraction of \(10\) from both sides:
\[d + 10 - 10 = 829 - 10\]
This simplifies the equation to:
\[d = 819\]
Thus, the value of \(d\) is \(819\).
Examples
Solving linear equations is a fundamental skill used in many everyday situations. For example, if you know you had \(\$829\) in your bank account before making a purchase of \(\$10\), you would represent your current balance \(d\) by the equation \(d + 10 = 829\). By solving for \(d\), you find that your current balance is \(d = \boxed{819}\). This simple process is essential for budgeting, managing finances, and understanding relationships in various fields like physics and engineering.