12.jpeg "(5n+3)12")
Exploring the Expression (5n + 3)12
The expression (5n + 3)12 represents a simple algebraic expression, often encountered in basic algebra and arithmetic. This article aims to delve into understanding its structure, simplification, and potential applications.
Understanding the Expression
Structure:
- 5n: Represents the product of 5 and a variable 'n', representing an unknown value.
- +3: Represents a constant term.
- (5n + 3): The entire expression within the parenthesis indicates a binomial.
- 12: Represents a constant factor.
Interpretation:
The expression signifies multiplying the sum of '5 times an unknown value (n)' and 3 by the constant 12.
Simplifying the Expression
To simplify the expression, we can distribute the 12 across the terms within the parenthesis:
(5n + 3)12 = 12(5n) + 12(3)
This simplifies to:
60n + 36
Therefore, the simplified form of the expression (5n + 3)12 is 60n + 36.
Applications
The expression (5n + 3)12 can be used in various scenarios, including:
- Modeling real-world situations: Imagine calculating the total cost of buying 'n' items that cost $5 each, plus a fixed cost of $3, then multiplying the total cost by 12.
- Evaluating expressions: If we are given a specific value for 'n', we can substitute it into the expression and evaluate it. For example, if n = 2, the expression becomes 60(2) + 36 = 156.
- Solving equations: The expression can appear in equations where we need to solve for the unknown 'n'.
Conclusion
The expression (5n + 3)12, though seemingly simple, represents a fundamental concept in algebra. Understanding its structure, simplification, and applications allows us to utilize it effectively in various contexts, from basic problem-solving to modeling real-world scenarios.