−3.6−1.9t+1.2+5.1t

Mac Grediser

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27-11-2024

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Simplifying Algebraic Expressions: A Step-by-Step Guide to Solving -3.6 - 1.9t + 1.2 + 5.1t

Algebraic expressions, like the one presented here (-3.6 - 1.9t + 1.2 + 5.1t), might seem daunting at first. However, with a systematic approach, simplifying them becomes straightforward. This article will guide you through the process of simplifying the given expression, explaining each step along the way.

Understanding the Expression

The expression -3.6 - 1.9t + 1.2 + 5.1t contains:

• Constants: These are the numbers without variables (-3.6 and 1.2).
• Variables: This is the 't' term, representing an unknown quantity.
• Coefficients: These are the numbers multiplying the variables (-1.9 and 5.1).

Simplifying the Expression

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, we have two types of like terms:

1. Constant terms: -3.6 and 1.2
2. 't' terms: -1.9t and 5.1t

Step 1: Combine the constant terms:

-3.6 + 1.2 = -2.4

Step 2: Combine the 't' terms:

-1.9t + 5.1t = 3.2t

Step 3: Combine the simplified terms:

Now that we've combined like terms, we can write the simplified expression:

-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 customary to write the term with the variable first.

Further Applications:

Simplifying algebraic expressions is a fundamental skill in algebra. It's crucial for solving equations, graphing functions, and tackling more complex mathematical problems. Mastering this skill will lay a solid foundation for your future algebraic studies.

Practice Problems:

Try simplifying these expressions using the same method:

1. 5x + 2 - 3x + 7
2. -2.5y + 4.1 + 1.5y - 8.6

By practicing these examples, you'll solidify your understanding of combining like terms and simplifying algebraic expressions. Remember, the key is to systematically identify and combine like terms to arrive at the most simplified form of the expression.