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

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Recognize that the expression involves the absolute value function and a negative sign: \(- |5|\).

Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative. So, \(|5| = 5\).

Substitute the absolute value back into the expression: \(- |5| = -5\).

Understand that the negative sign outside the absolute value changes the sign of the result from positive to negative.

Therefore, the expression simplifies to \(-5\).

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Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |5| equals 5, and |-5| also equals 5. It essentially removes any negative sign from the number.

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Evaluating Expressions

Evaluating an expression means calculating its value by following mathematical operations and rules. In this case, evaluating |-5| involves applying the absolute value operation to the number -5 to find its magnitude.

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Properties of Real Numbers

Understanding properties of real numbers, such as the fact that absolute value outputs are always non-negative, helps in correctly interpreting and simplifying expressions. This ensures accurate evaluation of expressions involving absolute values.

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