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

Verified step by step guidance

1. Recognize that the expression involves the absolute value function, denoted by vertical bars \(|\cdot|\), which gives the non-negative value of the number inside it.
2. Recall the definition of absolute value: for any real number \(x\), \(|x| = x\) if \(x \geq 0\), and \(|x| = -x\) if \(x < 0\).
3. Identify the number inside the absolute value: here it is \(-8\), which is less than zero.
4. Apply the absolute value definition for negative numbers: \(|-8| = -(-8)\).
5. Simplify the expression by removing the double negative to find 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 always non-negative, so |-8| equals 8. This concept helps in understanding magnitude without considering sign.

Number Line Representation

Visualizing numbers on a number line aids in grasping absolute value. Negative numbers lie to the left of zero, and their absolute value corresponds to the positive distance from zero, reinforcing the idea that absolute value measures magnitude only.

Basic Arithmetic Operations

Understanding how to evaluate expressions involves applying arithmetic rules correctly. For absolute value, this means recognizing that the operation transforms negative inputs into positive outputs, which is essential for simplifying and solving expressions.