Verified Answer :

  • To solve the equation \(-215 = r + 542\), subtract \(542\) from both sides to isolate the variable \(r\).
  • Simplify the expression: \(r = -215 - 542\).
  • Perform the arithmetic calculation to find \(r = -757\).
  • The final solution is \(\boxed{-757}\).

Explanation

  1. Understanding the Problem and Data Analysis

To solve for the variable \(r\) in the equation \(-215 = r + 542\), we need to isolate \(r\) on one side of the equation. This is a linear equation in one variable, and we can solve it by subtracting the same value from both sides to keep the equality balanced.

  1. Solving for r

To isolate \(r\), we subtract \(542\) from both sides of the equation:
\[-215 - 542 = r + 542 - 542\]
\[-215 - 542 = r\]
Now, we perform the subtraction of the two numbers. Since both numbers are negative, we are effectively adding their absolute values and keeping the negative sign:
\[r = -(215 + 542)\]
Calculating the sum: \(215 + 542 = 757\).
Therefore, \(r = -757\).

  1. Final Conclusion

We have successfully isolated \(r\) and found its value by performing simple arithmetic operations on the given constants. The final result is \(r = -757\).

Examples

Imagine you have a bank account balance represented by the equation \(r + 542 = -215\), where \(r\) is your initial balance and \(542\) is a deposit. To find your starting balance, you need to subtract the deposit from your current balance of \(-215\). This simple algebraic rearrangement allows you to track changes in values effectively in your daily financial life.

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