- Simplify the equation by adding 840 to both sides: \(d = -81 + 840\).
- Perform the arithmetic calculation: \(840 - 81 = 759\).
- The final value is \(d = \boxed{759}\).
Explanation
- Analyzing the Equation
The equation provided is \(d + (-840) = -81\). Our goal is to isolate the variable \(d\) to find its value. This is a linear equation in one variable, where we have a constant term subtracted from the variable \(d\). To solve for \(d\), we need to perform the same operation on both sides of the equation to maintain equality.
- Solving for d
To isolate \(d\), we add 840 to both sides of the equation:
\[d - 840 + 840 = -81 + 840\]
This simplifies to:
\[d = -81 + 840\]
Now, we perform the addition of the numbers on the right side. Starting with -81 and adding 840 is equivalent to calculating \(840 - 81\).
Calculating \(840 - 81 = 759\).
Therefore, \(d = 759\).
Examples
Suppose you have a bank account balance, and you know that after a transaction of -\$840, your new balance is -\$81. You can use this linear equation to find your original account balance \(d\) before the transaction. Solving for \(d\) in the equation \(d - 840 = -81\) helps you reconcile your financial records and ensure your accounting is accurate.