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

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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