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Simplifying mathematical expressions makes them easier to work with. This process involves reducing complex equations or formulas into simpler forms.
For example, consider the expression: $$9 - 6(7n - 5)$$.
Following the step-by-step solution, we first identify the distributive property and apply it. This property helps us distribute multiplication over addition or subtraction inside parentheses.
Let's expand and simplify: \( -6 \times (7n - 5) \) gives us \( -6 \times 7n + (-6) \times (-5) = -42n + 30 \). The original expression changes to: $$9 - 42n + 30$$.
Finally, we combine all like terms to get a simplified expression: $$39 - 42n$$.

Combining like terms is an essential step in simplifying expressions. Like terms are terms that have the same variables raised to the same power but can have different coefficients. This step helps us to consolidate and simplify the given expression further.
In the given problem, the final expanded expression was: $$9 - 42n + 30$$.
We need to combine the constant terms and the variable terms to simplify it:

• Constant terms here are 9 and 30.
• They get added together to give 39.

This results in the new expression: $$39 - 42n$$.
Combining like terms significantly reduces the complexity of the expression, making it easier to solve or further manipulate in equations.

Algebraic operations include addition, subtraction, multiplication, and division involving variables and constants. Understanding how to correctly perform these operations is crucial for simplifying expressions and solving equations.
In the problem: $$9 - 6(7n - 5)$$, various algebraic operations are used:

• Multiplication (Distributive Property): Expanding \( -6(7n - 5) \) to \( -42n + 30 \).
• Subtraction: Incorporating the distributed terms into the main expression by subtracting \( -6 \times 5 \) and dealing with \( -6 \times 7n \).
• Addition: Combining constants 9 and 30.

Mastering these basic operations allows for more complex mathematical problem-solving. Remember always to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to simplify expressions correctly.
Efficient use of algebraic operations enhances your ability to manipulate and solve any algebraic expression or equation, ensuring accurate results.