Verified Answer :

  • Recognize that subtracting a negative number is equivalent to adding a positive number, transforming the expression \(-14 - (-49)\) into \(-14 + 49\).
  • Perform the addition by calculating the difference \(49 - 14\).
  • The final result is \(\boxed{35}\).

Explanation

  1. Analyzing the Problem

The problem requires evaluating the expression \(-14 - (-49)\). We are subtracting a negative integer from another negative integer. The key principle here is the rule for subtracting negative numbers: for any two numbers \(a\) and \(b\), the expression \(a - (-b)\) is equivalent to \(a + b\). This is because subtracting a deficit is the same as adding a gain.

  1. Evaluating the Expression

Applying the property \(a - (-b) = a + b\), we substitute \(a = -14\) and \(b = 49\). The expression becomes:
\[-14 - (-49) = -14 + 49\]
To calculate this sum, we can rearrange the terms as:
\[49 - 14 = 35\]
Thus, \(-14 + 49 = 35\).

  1. Conclusion

We have successfully evaluated the expression. The subtraction of \(-49\) from \(-14\) simplifies to adding \(49\) to \(-14\), resulting in \(35\). Therefore, the final result is \(\boxed{35}\).

Examples

Consider a scenario where you have a bank account balance of -\$14, indicating you owe the bank \$14. If you receive a refund of \$49, you are essentially removing the debt of \$49 from your current financial state. Mathematically, this is represented by \(-14 - (-49)\). Adding the positive refund to your balance results in \(-14 + 49 = \$35\). This simple operation helps in tracking budgets and understanding how different transactions affect a total balance.

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