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The absolute value of a number represents its distance from zero on the number line, regardless of direction. It is always a non-negative number. The absolute value is denoted by vertical bars around the number, like this: \(|n|\). For example, \(|5| = 5\) and \(|-5| = 5\). In essence, absolute value strips away any negative sign, focusing solely on the magnitude of the number.

Consider the number \(-4\). Its absolute value is \(|-4|\), which equals 4. This happens because both 4 and -4 are 4 units away from zero, just in opposite directions.

Negative numbers are numbers less than zero, represented by a minus sign ( - ). They are the opposite of positive numbers. On the number line, positive numbers are to the right of zero, while negative numbers are to the left of zero.

When you take a negative number and apply the absolute value operation, you are essentially converting it to its positive counterpart. For example, taking \(-(-4)\) means flipping the sign, resulting in a positive 4. This is crucial when dealing with absolute values because the final result must be non-negative.

In our exercise, we started with \(-4\) as the given variable \(n\). The problem required us to find the absolute value of \(-n\), which is \(-(-4)\). Simplifying this results in the positive number 4.

Simplification in mathematics means reducing an expression to its simplest form. For absolute values, this often involves removing unnecessary signs and condensing the expression to a basic number.

In the given exercise, the process involved three steps:

• Identifying the absolute value of \(-n\).
• Flipping the sign of \(-4\) to obtain 4.
• Applying the absolute value bars to confirm the final result.

The absolute value of \(|4|\) is simply 4, thus the final, simplified answer is 4.

This step-by-step approach ensures clarity and accuracy in simplifying expressions involving absolute values, especially when they include negative numbers.