Evaluate each expression. See Example 5.|-8|

Verified step by step guidance

1. Identify the expression given: \(|-8|\).
2. Recall the definition of absolute value: The absolute value of a number is its distance from zero on the number line, regardless of direction.
3. Apply the definition: The absolute value of \(-8\) is the distance from \(-8\) to 0 on the number line.
4. Since distance is always positive, the absolute value of \(-8\) is the same as the absolute value of 8.
5. Conclude that \(|-8|\) is equal to 8.

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 two vertical bars surrounding the number, such as |x|. For example, |8| equals 8, and |-8| also equals 8, indicating that both numbers are 8 units away from zero.

Properties of Absolute Value

Absolute value has specific properties that are essential for evaluation. One key property is that |a| = a if a is non-negative, and |a| = -a if a is negative. This means that the absolute value function transforms negative inputs into positive outputs, which is crucial for solving expressions involving absolute values.

Evaluating Expressions

Evaluating expressions involves substituting values into mathematical expressions and simplifying them to find a numerical result. In the context of absolute values, this means applying the definition and properties of absolute value to compute the result of expressions like |-8|, ensuring a clear understanding of how to handle negative numbers.