Verified Answer :

  • Evaluate the expression inside the absolute value brackets: \(5 + 3 - 7 = 1\).
  • Apply the absolute value property \(|x| = x\) for \(x \ge 0\), so \(|1| = 1\).
  • Compare the result with the given choices.
  • The final answer is \(\boxed{D}\).

Explanation

  1. Analysis of the Expression

The problem asks us to evaluate the expression \(|5 + 3 - 7|\). We recognize that the expression involves an arithmetic operation contained within absolute value brackets. The notation \(|x|\) denotes the absolute value of a number \(x\), representing its distance from zero on the number line. The property of the absolute value is defined as \(|x| = x\) if \(x \geq 0\), and \(|x| = -x\) if \(x < 0\). Our goal is to determine the numerical value of the expression and select the correct option among the choices provided.

  1. Evaluating the Inside of the Absolute Value

To evaluate \(|5 + 3 - 7|\), we first perform the operations inside the absolute value bars. We add and subtract the numbers in order from left to right:
\[5 + 3 = 8\]
\[8 - 7 = 1\]
So, the expression inside the absolute value symbols simplifies to \(1\).

  1. Applying Absolute Value and Selecting the Correct Option

Now that we have the value inside the absolute value, we apply the definition:
\[|1|\]
Since \(1 \geq 0\), the absolute value of \(1\) is simply \(1\).
Comparing this result to the given options:

A\(-1\)
B\(-15\)
C\(15\)
D\(1\)

The calculated value \(1\) corresponds to option D.

Examples

Absolute values are commonly used in fields like physics and finance to represent magnitude regardless of direction or sign. For instance, if you measure the deviation of a manufacturing part from its specified size, you might get a result like \(|-0.5\text{ mm}|\), meaning the part is \(0.5\text{ mm}\) off in either direction. Similarly, in calculating the distance between two points on a number line, like the difference between \(-5\) and \(3\), we use \(|-5 - 3| = |-8| = 8\) to find that the distance is exactly \(8\) units.