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Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. They are used to describe relationships and changes, and they form the backbone of algebra. Unlike equations, they don't express equality but rather represent quantities that can vary or be unknown. In our example, 6-(-8) is an algebraic expression showing the operation of subtracting a negative number from a positive one.

Understanding algebraic expressions is crucial because they allow us to succinctly describe complex numerical situations. For instance, in our given expression, the positive integer 6 is being subtracted by a negative integer 8, creating the need to understand how to handle negatives in this context.

The rules for the addition and subtraction of integers are fundamental to correctly solving algebraic problems. Adding integers with the same sign means combining their absolute values, while adding integers with opposite signs involves finding the difference between their absolute values. As for subtraction, remember that subtracting an integer is the same as adding its opposite, making 6-(-8) become 6+8 after applying this rule.

Integers can be visualized on a number line, with subtraction of an integer being equivalent to moving in the opposite direction. This visualization helps to understand why subtracting a negative number actually increases the value, shifting our position to the right on the number line towards higher numbers.

Basic arithmetic operations include addition, subtraction, multiplication, and division. They serve as building blocks for more advanced math concepts. With addition, we combine quantities, while subtraction involves taking away. Multiplication can be seen as repeated addition, and division as the process of distributing a number into equal parts.

In our example 6-(-8), application of basic arithmetic starts with recognizing the subtraction of a negative number. Here, we applied the rule that subtracting a negative is equivalent to addition, transforming our expression into 6+8. The final addition yields 14, showcasing the importance of mastering these operations to simplify and solve algebraic expressions correctly.