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Understanding the order of operations is crucial for solving algebra problems correctly. The order of operations dictates the sequence in which you should perform each part of a mathematical expression. The common acronym for remembering this sequence is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 
In the given exercise, we apply the order of operations as follows:
- Resolve the expression inside the parentheses first.
- Then, perform any multiplication or division.
- Finally, handle any addition or subtraction.
Skipping or mixing up these steps can lead to incorrect answers, so always follow PEMDAS strictly.

Parentheses are used in algebra to indicate that operations inside them should be performed first. This grouping overrides the usual order of operations. In the given problem, you first need to solve what’s inside the parentheses: \(5 - 7 = -2\).
Once you have simplified the terms inside the parentheses, you can then proceed to the next steps according to the order of operations. Parentheses ensure clarity and help avoid ambiguity, making it easier to understand which parts of the expression need immediate attention.

Adding integers, especially when dealing with negative numbers, can be a bit tricky. An integer is simply a whole number, which can be positive, negative, or zero. In the example, the integer addition happens in the final step: \(-8 + (-8)\).
When adding a negative number to another negative number, you actually move further into the negative side of the number line. Here, \(-8 + (-8)\) results in \(-16\) because you move 8 units to the left from -8.
Think of it as owing money: if you owe \(8 and then borrow another \)8, you now owe $16. Understanding how to handle positive and negative integers is foundational for solving algebraic expressions correctly.