%2B(2y-3.5)%2B(-1%2F4x%2B5).jpeg "(7/4x-5)+(2y-3.5)+(-1/4x+5)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the algebraic expression: (7/4x - 5) + (2y - 3.5) + (-1/4x + 5)
Understanding the Expression
The expression contains multiple terms, each involving variables (x and y) and constants. Our goal is to combine like terms to simplify the expression.
Like terms are terms that have the same variable and the same exponent. For example, 7/4x and -1/4x are like terms because they both have 'x' to the power of 1.
Steps to Simplify
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Identify Like Terms:
- x terms: 7/4x and -1/4x
- y terms: 2y
- Constant terms: -5, -3.5, and 5
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Combine Like Terms:
- x terms: (7/4x) + (-1/4x) = 6/4x = 3/2x
- y terms: 2y (remains the same)
- Constant terms: (-5) + (-3.5) + (5) = -3.5
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Rewrite the Expression: The simplified expression is: (3/2x) + 2y - 3.5
Conclusion
By combining like terms, we have successfully simplified the expression. The simplified expression (3/2x) + 2y - 3.5 is equivalent to the original expression but is easier to work with and understand. This process of simplifying algebraic expressions is crucial in various mathematical and scientific fields.