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Negative numbers are numbers less than zero. They can be found on the left side of the number line. The most distinctive feature of negative numbers is their minus sign (-) before them. An important concept to understand is what happens when you negate a negative number. Negating a negative number means applying a negative sign to an already negative number, which effectively changes it into a positive number. For example:

• The negation of \(-2\) is \(-(-2) = 2\).
• The negation of \(-5\) is \(-(-5) = 5\).

Comprehending negative numbers helps in performing calculations that involve things like time before zero (BC years) and various real-world scenarios like temperature changes below zero or financial debts. It's fundamental to understanding more complex mathematical topics, including algebraic operations.

Simplifying expressions involves rewriting them in a way that makes complex equations more understandable and easier to work with. The goal is to make the expression as simple as possible without changing its value. Changes may include addressing operations like addition, subtraction, multiplication, and division, or dealing with negative signs.
To simplify expressions like the one given in the exercise, follow these guidelines:

• Address any operations within parentheses or other grouping symbols first.
• Resolve any negations or operations on negative numbers carefully.
• Finally, apply any remaining operations, like absolute values, to achieve the simplest form of the expression.

This process is essential for solving equations as it allows for a clearer view of the terms and their interactions, leading to more efficient problem-solving.

Algebraic operations involve a variety of basic arithmetic operations such as addition, subtraction, multiplication, and division, but they also extend to more complex processes like working with variables and expressions. These operations follow certain rules and properties, including the order of operations.
When you encounter an expression like \(-(-2)\), it's crucial to handle each operation step by step:

• Start by addressing any negations or absolute values first, as these can significantly alter the expression.
• Utilize the principles of the order of operations (parentheses first, exponents second, multiplication and division third, and addition and subtraction last) to simplify expressions properly.
• Create a routine practice of checking your results to ensure no mistakes were made during simplification or in applying operations.

Grasping algebraic operations is vital, as they are the foundation of algebra, allowing for more advanced work with equations, functions, and graphs.