Verified Answer :

  • Perform the subtraction inside the absolute value: \(2 - 6 = -4\).
  • Apply the property of the absolute value function: \(|-4| = 4\).
  • Compare with the given options to conclude the correct answer is \(4\).
  • Final result: \(\boxed{4}\).

Explanation

  1. Analyze the Expression Inside the Absolute Value

To evaluate the expression \(|2 - 6|\), we start by focusing on the operation inside the absolute value bars. The absolute value of a real number, denoted by \(|x|\), represents its distance from zero on the number line. By definition, \(|x| = x\) if \(x \geq 0\), and \(|x| = -x\) if \(x < 0\). First, perform the subtraction within the bars: \(2 - 6 = -4\).

  1. Apply the Absolute Value Definition

Now that we have the result of the subtraction, which is \(-4\), we apply the definition of the absolute value. Since \(-4 < 0\), we have \(|-4| = -(-4)\). According to the rules of arithmetic, the negative of a negative number is the corresponding positive number: \(-(-4) = 4\). Thus, \(|2 - 6| = 4\). Comparing this result to the given options, we identify that the correct choice is option A.

Examples

Absolute value is frequently used in real-life situations to calculate distances, differences, or margins of error, where the direction or sign does not matter. For instance, if you are checking the difference in temperature between a cold morning at \(2^\circ C\) and a chilly afternoon at \(6^\circ C\), the temperature change is \(|2 - 6| = 4^\circ C\). Regardless of whether the temperature went up or down, the magnitude of the change remains a positive quantity, which is essential for reporting physical measurements accurately.

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