- Start with the equation \(w - 50 = 941\).
- Add \(50\) to both sides to isolate the variable \(w\).
- Perform the arithmetic calculation \(941 + 50 = 991\).
- Conclude that the solution is \(w = \boxed{991}\).
Explanation
- Analysis of the Equation
We are tasked with solving the linear equation \(w - 50 = 941\) for the variable \(w\). Our primary goal is to isolate \(w\) on one side of the equation. This involves moving the constant term \(-50\) to the other side, which we accomplish by applying the inverse operation, addition, to both sides of the equation.
- Isolating the Variable w
To isolate \(w\), we add \(50\) to both sides of the given equation:
\[w - 50 + 50 = 941 + 50\]
This simplifies the left side because \(-50 + 50 = 0\), effectively isolating \(w\):
\[w = 941 + 50\]
- Final Calculation and Result
Now, we perform the addition on the right-hand side of the equation:
\[w = 991\]
Thus, the value of \(w\) that satisfies the original equation is \(991\).
Examples
Linear equations like this appear frequently in financial planning. For instance, if you have a budget balance \(w\) and you pay off a bill of \(\$50\), leaving you with \(\$941\), you can calculate your initial balance using the equation \(w - 50 = 941\). By adding the expense back to the remaining amount, you determine that you started with \(\$991\).