(7×+2)-(3×-1)

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Jun 07, 2024

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Simplifying Algebraic Expressions: (7x + 2) - (3x - 1)

When working with algebraic expressions, it's essential to master the skills of simplifying and manipulating expressions to reveal their underlying structure. In this article, we'll focus on simplifying the expression (7x + 2) - (3x - 1).

Understanding the Expression

Before we dive into simplifying the expression, let's take a moment to understand what we're working with:

(7x + 2) - (3x - 1)

This expression consists of two parts:

• (7x + 2): This part of the expression represents a sum of two terms: 7x and 2.
• -(3x - 1): This part of the expression represents a difference: subtract 3x minus 1 from the previous result.

Simplifying the Expression

To simplify the expression, we'll follow the order of operations (PEMDAS):

1. Distribute the negative sign: -(3x - 1) = -3x + 1 (distribute the negative sign to both terms inside the parentheses)
2. Combine like terms: (7x + 2) - 3x + 1 = 7x - 3x + 2 + 1 (combine like terms x and constants)
3. Simplify further: 4x + 3 (combine the x terms and add the constants)

The Simplified Expression

After simplifying the expression, we arrive at:

(7x + 2) - (3x - 1) = 4x + 3

This simplified expression reveals the underlying structure of the original expression, making it easier to work with and analyze.

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, enabling us to uncover the underlying structure of complex expressions. By following the order of operations and combining like terms, we can reduce complex expressions to their simplest form, making them easier to work with and understand.