Evaluate each expression. |-4|

Verified step by step guidance

1. Recognize that the expression involves the absolute value function, denoted by vertical bars \(|\cdot|\), which measures the distance of a number from zero on the number line.
2. Recall that the absolute value of a number is always non-negative, meaning \(|a| \geq 0\) for any real number \(a\).
3. Identify the number inside the absolute value: here it is \(-4\).
4. Apply the definition of absolute value: \(|-4|\) is the distance of \(-4\) from zero, which is the positive value \(4\).
5. Conclude that the absolute value expression simplifies to \(4\).

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. For example, |-4| equals 4 because -4 is four units away from zero.

Properties of Real Numbers

Real numbers include all rational and irrational numbers. Understanding their properties, such as how absolute value interacts with positive and negative numbers, helps in evaluating expressions correctly.

Evaluating Expressions

Evaluating an expression means simplifying it to a single value by applying mathematical operations and rules. For absolute value expressions, this involves removing the absolute value bars by determining the non-negative equivalent.