Verified Answer :

  • Understand that the absolute value of a negative number is its positive counterpart: \(|-3| = 3\) and \(|-5| = 5\).
  • Add the resulting positive values to evaluate the final expression: \(3 + 5 = 8\).
  • Compare the sum to the given options to confirm that the correct choice is D.
  • Final result: \(\boxed{8}\).

Explanation

  1. Understanding Absolute Value

The absolute value of a real number, denoted by \(|x|\), represents the distance of the number from zero on the number line. Consequently, the absolute value of any real number is always non-negative. Specifically:

  • If \(x \ge 0\), then \(|x| = x\).
  • If \(x < 0\), then \(|x| = -x\).

Our objective is to calculate the expression \(|-3| + |-5|\).

  1. Evaluating the Expression

To solve the problem, we evaluate each absolute value term independently:

  • For \(|-3|\), since \(-3 < 0\), we apply the rule \(|-x| = x\) for \(x > 0\), yielding \(|-3| = 3\).
  • For \(|-5|\), since \(-5 < 0\), we apply the same rule to get \(|-5| = 5\).

Now, we add these results together:
\[|-3| + |-5| = 3 + 5 = 8\]

  1. Final Answer Selection

Comparing the calculated result, \(8\), to the given options:

  • A. \(-2\)
  • B. \(-8\)
  • C. \(2\)
  • D. \(8\)

The calculated result matches option D. Thus, the value of the expression is \(\boxed{8}\).

Examples

Absolute values are essential when calculating distances or differences where the direction doesn't matter. For example, if you are calculating the distance between two houses located at -3 km and -5 km relative to a reference point, you are effectively finding the sum of the absolute values of their positions: \(|-3| + |-5| = 8\) km. This ensures that the distance is always represented as a positive quantity.

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