Verified Answer :

  • Set up the equation \(38 + x = 0\) to find the unknown value \(x\).
  • Solve the equation by subtracting 38 from both sides to get \(x = -38\).
  • Evaluate the provided options: A (\(38\)), B (\(38\)), C (\(\frac{1}{38}\)), and D (\(-38\)).
  • Identify option D as the only value equal to \(-38\), so the correct answer is \(\boxed{D}\).

Explanation

  1. Analyzing the Problem and Solving the Equation

The goal is to find a number \(x\) that, when added to \(38\), results in a sum of \(0\). Mathematically, this can be represented by the linear equation:
\[38 + x = 0\]
To solve for \(x\), we subtract \(38\) from both sides of the equation:
\[x = 0 - 38\]
\[x = -38\]
Thus, the number that must be added to \(38\) to reach \(0\) is \(-38\).

  1. Evaluating the Given Options

Now, we examine the given options to identify which one equals \(-38\):

  • Option A: \(|38| = 38\)
  • Option B: \(|-38| = 38\)
  • Option C: \(\frac{1}{38} \approx 0.026\)
  • Option D: \(-38 = -38\)

Comparing these values with our result of \(-38\), we see that only option D matches our calculated value.

  1. Conclusion

Based on the calculation and the comparison with the provided choices, the correct number to add to \(38\) to obtain a sum of \(0\) is \(-38\), which corresponds to option D.
\(\boxed{D}\)

Examples

This concept of finding the "additive inverse" is essential in balancing accounts or equations in daily life. For instance, if you have a debt of \(\$38\), you need an asset of \(\$38\) to bring your net balance to \(\$0\). Similarly, if a temperature is \(38^\circ\) above freezing, the additive inverse \(-38^\circ\) represents the cooling required to reach the freezing point of \(0^\circ\). Understanding how to balance these quantities is a fundamental skill in finance, physics, and basic arithmetic.

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