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The operation of subtraction is one of the basic arithmetic operations in math. It involves finding the difference between numbers. In the context of algebra and dealing with negative numbers, subtraction can have an interesting twist. When you subtract a negative number from another number, you are essentially adding its opposite, which is a positive number.

For example, if we have the expression \( -8-(-12) \), it might seem puzzling at first. Remember that subtracting a negative is like adding a positive. Hence, this expression simplifies to \( -8 + 12 \). This is because the two minuses cancel each other out, turning the operation into addition. This concept is crucial in understanding how to handle similar situations in algebraic expressions.

Simplifying expressions is a way of rewriting them so they are easier to understand and solve. It involves combining like terms and reducing expressions to their simplest form. When faced with an algebraic expression that includes both negative and positive numbers, we aim to combine like terms to make the expression as simple as possible.

Consider the earlier step where we turned \( -8-(-12) \) into \( -8 + 12\). This is now a simpler expression with only one operation to perform. We can also apply this concept when dealing with variables and more complicated equations. Simplifying expressions is not only about making them easier to read; it also sets the stage for more advanced operations in algebra, such as solving equations or inequalities.

Performing addition is one of the first operations we learn in math, but it can still pose challenges when working within the real numbers, which include positive and negative values. After simplifying an expression, we often reach a stage where we need to combine the numbers we are left with.

In our initial example, after simplifying we had \( -8 + 12 \) which gave us 4. At this point, we need to add 3 to our result, following the original expression \( -8 - (-12) + 3 \). Thus, we perform the final addition: \( 4 + 3 \) to obtain 7. This example shows that being comfortable with basic addition, not only with positive integers but also with incorporating negative values, is essential for evaluating algebraic expressions effectively.