Verified Answer :

  • Define the absolute value: the distance of a number from zero, always resulting in a non-negative value.
  • Evaluate individual components: \(|-6| = 6\) and \(|-3| = 3\).
  • Multiply the results: \(6 \times 3 = 18\).
  • Match with options: The result corresponds to option C, \(\boxed{18}\).

Explanation

  1. Analysis of the Absolute Value Operation

The expression to evaluate is \(|-6| \times |-3|\). The absolute value function, denoted by \(|x|\), represents the non-negative magnitude of a real number \(x\). Its definition is:
\[|x| = \begin{cases} x & \text{if } x \ge 0 \ -x & \text{if } x < 0 \end{cases}\]
This means the absolute value of a negative number is its positive counterpart. We need to evaluate the absolute value of each term individually before multiplying them.

  1. Calculating the Numerical Result

We have two terms: \(|-6|\) and \(|-3|\).

  • For the first term, since \(-6 < 0\), the absolute value is \(|-6| = -(-6) = 6\).
  • For the second term, since \(-3 < 0\), the absolute value is \(|-3| = -(-3) = 3\).

Now, we substitute these values back into the expression:
\[|-6| \times |-3| = 6 \times 3 = 18.\]

  1. Comparison with Options and Final Conclusion

Comparing our result of \(18\) to the given options:
◯ A. \(-18\)
◯ B. \(9\)
◯ C. \(18\)
◯ D. \(-9\)
The computed result matches option C. Thus, the final answer is 18.

Examples

Absolute value is used in real life to represent distances, which are always non-negative. For instance, if you are located at position \(-6\) on a line and need to travel to the origin \(0\), the distance is \(|0 - (-6)| = |6| = 6\) units. Similarly, if you are at \(-3\), the distance to the origin is \(3\) units. When calculating combinations of these distances or magnitudes, the absolute value ensures that negative positions do not result in negative measurements.

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