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A number line is a straight horizontal line on which numbers are placed at equal intervals. It's a simple yet powerful visual tool that helps in understanding the position and relationship of numbers.

When you look at a number line, the zero is usually located in the center. Numbers to the right of zero are positive, while those to the left are negative. By understanding this, you can easily identify the position of any number. For example, -5 is five units left of zero, and 8 is eight units right of zero.

On the number line, absolute value is represented by the distance a number is from zero, regardless of direction. So, whether it's -5 or +5, the absolute value is 5 in both cases. This is because each is five units away from zero.

Positive numbers are the numbers that are greater than zero. They often appear to the right of zero when placed on a number line. These numbers are used in many aspects of mathematics to denote values that increase or grow.

Some key points about positive numbers include:

• They are always greater than negative numbers and zero.
• They represent gain, such as profit, or attributes like height and distance.

In our current context, the absolute value of a number is always a positive number. Therefore, when evaluating expressions like \(|-5|\) or \(|-8|\), we turn these into their positive counterparts: 5 and 8, respectively.

Adding integers may initially seem tricky, especially when dealing with negative numbers, but the concept becomes straightforward with practice.

To add integers:

• When combining two positive integers, the result is the sum of the two numbers. For example, 2 + 3 = 5.
• When combining two negative integers, you add their absolute values and then apply a negative sign. For example, -2 + -4 becomes -6.
• When you add a positive integer to a negative one, you are essentially subtracting. For example, 5 + (-3) equals 2, as you move left on the number line.

In problems involving absolute values, such as \(|-5| + |-8|\), you add the positive results of the absolute values. Therefore, \(|-5| = 5\) and \(|-8| = 8\), so the final step in the solution is simply adding, which is 5 + 8 = 13.