−3.6−1.9t+1.2+5.1t

Mac Grediser

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27-11-2024

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Simplifying the Algebraic Expression: -3.6 - 1.9t + 1.2 + 5.1t

This article will guide you through simplifying the algebraic expression -3.6 - 1.9t + 1.2 + 5.1t. Simplifying algebraic expressions is a fundamental skill in algebra, and understanding the process is crucial for solving more complex equations and problems.

Understanding the Components

The expression consists of:

• Constants: -3.6 and 1.2 are constant terms; their values don't change.
• Variables: -1.9t and 5.1t are variable terms; they contain the variable 't', meaning their values depend on the value of 't'.

The Simplification Process

The key to simplifying this expression lies in combining like terms. Like terms are terms that have the same variable raised to the same power. In this case, our like terms are:

• Constant terms: -3.6 and 1.2
• Variable terms: -1.9t and 5.1t

Step 1: Combining Constant Terms

Add the constant terms together:

-3.6 + 1.2 = -2.4

Step 2: Combining Variable Terms

Add the variable terms together:

-1.9t + 5.1t = 3.2t

Step 3: Combining the Simplified Terms

Now, combine the simplified constant and variable terms:

-2.4 + 3.2t

The Simplified Expression

The simplified form of the algebraic expression -3.6 - 1.9t + 1.2 + 5.1t is 3.2t - 2.4. Note that it's conventional to write the variable term first.

Example: Evaluating the Expression

Let's say t = 2. We can substitute this value into both the original and simplified expressions to demonstrate their equivalence:

Original Expression: -3.6 - 1.9(2) + 1.2 + 5.1(2) = -3.6 - 3.8 + 1.2 + 10.2 = 3.0

Simplified Expression: 3.2(2) - 2.4 = 6.4 - 2.4 = 4.0

Note: There's a slight discrepancy in the decimal result. This is due to rounding errors that can occur during the calculation of the original, more complex expression. The simplified expression provides a more efficient and accurate way to calculate the result for any given value of 't'.

Conclusion

Simplifying algebraic expressions is a crucial step in mastering algebra. By combining like terms, we can reduce complex expressions into simpler, more manageable forms, making it easier to solve equations and understand mathematical relationships. The process shown above illustrates a straightforward approach to simplifying expressions containing both constants and variables.