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When working with algebraic expressions, one fundamental rule is the **Order of Operations**. This rule ensures that everyone solves the expression the same way and gets the correct answer. It's often remembered by the acronym PEMDAS, which stands for:

• Parentheses
• Exponents (powers and roots, etc.)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In the given expression 5-3[6-(2+7)] , we first perform operations inside parentheses and brackets, as per PEMDAS. That means, we first add 2+7 to get 9 , and then substitute inside the brackets. This rule helps maintain clarity in problem-solving, allowing us to systematically break down and solve complex expressions step by step.
The practice not only aids in accurate computing but ensures consistency across different solvers and contexts.

**Parentheses and brackets** are vital tools in algebra that signal which parts of an expression should be calculated first. In the equation 5-3[6-(2+7)] , both parentheses ( ) and brackets [ ] are present, helping to organize operations.

• Parentheses: Operations within parentheses take the highest priority. We solve whatever is enclosed first; in this case, (2 + 7) becomes 9.
• Brackets: These are used to further clarify operations, often used when a second set of grouping is required in an expression. After simplifying the parentheses, the expression inside the brackets 6-9 is simplified next, which yields -3.

By using both grouping symbols, we ensure the expression is simplified correctly and in the intended order, enabling precise calculations in more complex problems.

Dealing with **negative numbers** in algebra can be tricky, but it's crucial to understand how they operate in expressions. In the expression 5-3(-3) , the negative sign outside the brackets indicates a multiplication by a negative number. This transforms the expression -3(-3) into a positive result: 9.

• Multiplying two negative numbers makes a positive result. For instance, -3 times -3 gives 9.
• When subtracting a negative number, it effectively becomes addition. Thus, the expression 5 - (-9) converts to 5 + 9.

Understanding how negatives interact in algebra is important for simplifying expressions correctly and preventing errors in calculations. Keeping track of the signs during each step of simplification ensures you arrive at the correct final answer.