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The number line is a fundamental visual aid used to represent numbers as a straight, horizontal line with equally spaced segments. On a number line, positive numbers are placed to the right of zero and negative numbers are placed to the left. The number line helps us understand the concept of absolute value as it illustrates the position of numbers relative to zero.

When looking at a number line, we can quickly see that the absolute value of a number is its distance from zero, without considering direction. For instance, both 5 and -5 are at a distance of 5 units from zero. They simply lie in opposite directions; 5 to the right and -5 to the left. Visualizing absolute values on the number line, therefore, makes it clear that both will have an absolute value of 5, since distance is always expressed as a non-negative number.

Distance from zero, often mentioned in the context of a number line, is another way to describe absolute value. It represents how far a number is from the point marked as zero on the number line. Importantly, this 'distance' is always a non-negative value, regardless of which direction you move on the line.

To further clarify, consider any point on the number line, say -3. Although -3 is to the left of zero and is considered negative in value, its distance from zero is 3 units. Similarly, the point +3 is also 3 units from zero but to the right. Therefore, the absolute value, |3| or |-3| both equate to 3, emphasizing the non-directional nature of absolute value. Remember, distance can never be negative!

Evaluating expressions that include absolute values involves identifying the numerical value that the expression represents. For the purpose of understanding how to evaluate such expressions, let's recall that the basic idea of absolute value is to determine the distance from zero regardless of direction. As such, when an expression contains absolute values, each term within the absolute value signs is evaluated in terms of how far it is from zero on a number line.

Let's take the expression from the exercise, '|5| + |-6|'. When evaluating the expression, we're looking for the 'positive equivalents' of these numbers, as absolute values convert all numbers to their non-negative counterparts. Firstly, since 5 is already positive, its absolute value remains 5. Secondly, -6 is negative, so we take its positive counterpart which is 6. We then add these distances together: 5 (for |5|), plus 6 (for |-6|), giving us a total of 11. The process of evaluating expressions with absolute values is crucial for understanding how to handle both positive and negative terms in broader mathematical contexts.