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The number line is a visual representation of numbers arranged in a straight line. Each point corresponds to a number, and this helps us understand the concept of positioning in mathematics.

For example, if you start at zero, positive numbers are placed to the right of it (1, 2, 3, etc.), and negative numbers are to the left of zero (-1, -2, -3, etc.).

To understand the absolute value, think of the number line as a measuring tape. The absolute value measures how far a number is from zero, without worrying about which side of zero the number is on.

By the way, if you look at -14 on the number line, it is 14 units to the left of zero. Its distance to zero is 14, regardless of the direction.

In mathematics, non-negative numbers are those that are either greater than or equal to zero. This means that they can be positive or zero, but not negative.

The absolute value of any number is always non-negative because it represents a distance, which cannot be negative. For example, whether we are calculating \(|-14|\) or \(|14|\), the result will always be 14, a non-negative number.

Remember, the concept of absolute value strictly deals with magnitude and ignores any negative signs. This leads to the result being either zero or positive.

Simplification in mathematics means making an expression easier to understand or solve. In the case of absolute values, simplification involves finding the distance of a number from zero.

The fundamental steps to simplify an absolute value expression are:

• Identify the number inside the absolute value signs.
• Determine its distance from zero on the number line.
• Write the result as a non-negative number.

Let's review our example. For \(|-14|\), we recognize that -14 is 14 units away from zero. We disregard the negative sign and note the distance, which gives us the non-negative result of 14. Thus, the simplification of \(|-14|\) is simply 14.