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Understanding how to combine numbers through addition and subtraction is fundamental in simplifying algebraic expressions. The process might seem straightforward when dealing with positive numbers, but it can become a bit trickier when negatives are involved.

Imagine you're keeping a score in a game: if you gain points (addition) and lose points (subtraction), you would calculate your total score by adding and subtracting values in the order they occurred. The same principle applies to algebraic expressions. When you see a problem like \(13 - 2 - (-8)\), you start at the left and work your way to the right. The operation begins with the first two numbers, \(13 - 2\), which straightforwardly gives 11.

It's crucial to perform these operations in sequence and also to consider the signs of the numbers you're adding or subtracting to maintain accuracy in your calculations.

Handling negative numbers can sometimes cause confusion. However, there's a simple rule that can make dealing with them much easier: subtracting a negative number is the same as adding its positive counterpart. This is because a negative symbol in front of another negative symbol effectively turns the operation into an addition.

For example, let's look at the expression \(-(-8)\). The two negative signs cancel each other out, so it's as if you're looking at a plus sign in front of the 8. Thus, \(-(-8)\) becomes simply \(+8\). When you encounter this in an expression, like in the given problem, you apply this concept to find that \(13 - 2 - (-8)\) becomes \(13 - 2 + 8\). By remembering this rule, you can significantly simplify the process of working with negative numbers.

When performing arithmetic operations, there's a specific order you must follow to ensure that you get the correct result. This sequence is often taught using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In the context of the provided exercise, there are no parentheses or exponents, so you go straight to dealing with addition and subtraction. You perform these operations from left to right. The expression \(13 - 2 - (-8)\) must be addressed in two steps - first by calculating \(13 - 2\), and then by incorporating the next number in line, which is -(-8), or simply +8. By following these rules systematically, you ensure that you simplify the algebraic expression correctly.