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Grouping symbols are essential in determining the order of operations in mathematical expressions. These symbols include parentheses \(( )\), brackets \([ ]\), and braces \(\{ \}\). They help to organize calculations by specifying which operations should be performed first.
When an expression contains multiple sets of grouping symbols, work from the innermost to the outermost group. This ensures that you evaluate smaller, manageable chunks first, leading to a correct overall result.
In the example exercise, parentheses were used first, followed by brackets and finally braces. This hierarchical approach helps in systematically solving complex expressions.

Elementary algebra involves using variables and operations to explore mathematical relationships. It forms the foundation for more advanced mathematical concepts, providing the rules for manipulating equations and expressions.
The order of operations is a key principle in algebra, guiding which operations to complete first. It is often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
By applying algebraic rules, you ensure expressions with multiple operations are solved consistently and correctly. In the exercise given, the systematic application of algebraic operations to expressions like \(6\{2[2(10-9)]\}\) was essential to reach the correct outcome.

A step-by-step solution breaks down the problem-solving process into manageable parts, guiding you through each stage of solving an expression. This method is especially helpful for understanding how to apply mathematical concepts effectively.

• Step 1: Innermost Group - Start with the innermost grouping symbol, usually parentheses. Calculate what's inside them first.
• Step 2: Next Level Group - Move to the next level of grouping symbols, such as brackets or braces, and solve the expression within.
• Step 3: Outer Group - Finally, address the outer grouping symbol and complete the remaining operations.
• Step 4: Simplify - With all grouping symbols handled, simplify the expression to find the solution.

This approach prevents errors and builds a clear path to finding the right answer, as demonstrated by successfully solving the operation to arrive at 24 in the given exercise.