Evaluate each expression. See Example 5.-|5|

Verified step by step guidance

1. Identify the absolute value expression: \(|5|\).
2. Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative.
3. Evaluate the absolute value: \(|5| = 5\).
4. Apply the negative sign outside the absolute value: \(-|5| = -5\).
5. Conclude that the expression evaluates to the negative of the absolute value.

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |5| equals 5, while |-5| also equals 5, illustrating that both positive and negative values yield the same absolute value.

Evaluating Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify the expression to a single numerical value. In this case, evaluating |5| requires recognizing that it is already a constant, leading directly to the result without further calculations.

Properties of Numbers

Understanding the properties of numbers, such as the identity property and the concept of non-negativity, is essential in evaluating expressions. The identity property states that any number added to zero remains unchanged, and since absolute values are defined to be non-negative, this property helps clarify the outcome of expressions involving absolute values.