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Understanding the concept of the number line is crucial when dealing with absolute values. A number line is a visual representation of numbers placed in order. You can imagine it as a horizontal line where each point corresponds to a number. The center of the number line is zero. Positive numbers are placed to the right of zero, and negative numbers are placed to the left of zero.

Absolute value measures the distance of any number from zero. The beauty of the number line is that it lets you visualize this distance directly, regardless of whether the number is positive or negative. For example, the distance from 0 to 11 and from 0 to -11 is the same on a number line, which is 11 units. So, \( |11| \) and \( |-11| \) both equal 11.

Mathematical notation is a language of its own. To express absolute value, we use specific symbols. The absolute value of a number is represented by placing the number between two vertical bars. For example, the absolute value of 11 is written as \( |11| \). This way of writing makes it easy to recognize absolute values in equations and calculations.

Using proper notation is not just about correctness; it also helps in avoiding confusion, especially when dealing with more complex equations that involve absolute values. Remember, no matter the number inside the bars, the absolute value is always non-negative.

One essential aspect of absolute values is that they are always non-negative. A non-negative number is any number that is greater than or equal to zero. This means that it can either be zero or any positive number. Since absolute value represents distance, and distance can't be negative, absolute values are inherently non-negative.

For example, both \( |11| \) and \( |-11| \) yield 11. The concept of non-negative numbers ensures clarity when comparing magnitudes. It’s also why absolute value is so useful in real-life situations like measuring distance, where direction does not matter, only the magnitude does.