Verified Answer :

  • Begin with the original equation: \(283 = 29 - y\).
  • Isolate the variable \(y\) by adding it to both sides and subtracting \(283\) from both sides: \(y = 29 - 283\).
  • Perform the subtraction to find the value: \(y = -254\).
  • The final answer is \(\boxed{-254}\).

Explanation

  1. Analysis of the Equation

The problem asks us to solve for the variable \(y\) in the linear equation \(283 = 29 - y\). This is an algebraic equation where we need to isolate the variable \(y\) to find its value. By applying basic arithmetic principles and algebraic operations, we can determine the solution.

  1. Isolating the Variable y

To isolate the variable \(y\), we first add \(y\) to both sides of the equation:
\[283 + y = 29 - y + y\]
This simplifies to:
\[283 + y = 29\]
Next, we subtract \(283\) from both sides of the equation to isolate \(y\):
\[283 - 283 + y = 29 - 283\]
This gives us:
\[y = 29 - 283\]

  1. Calculating the Final Result

Now, we perform the final arithmetic operation to calculate the value of \(y\):
\[y = 29 - 283 = -254\]
Thus, the solution to the equation is \(y = -254\).

Examples

Solving equations is a fundamental skill in everyday budgeting. For instance, if you have a budget of \$29 for a specific expense, but you have already overspent by \$283 (resulting in a balance of \$283, which you represent as the debt or shortfall in your account), you can set up an equation to find out how much additional debt or negative balance occurred, just as we solved for \(y\) here. This helps in understanding and tracking your financial standing effectively.

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