0.18+y=0.4(7y–0.9)

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10-10-2024

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Solving for "y": A Step-by-Step Guide with Real-World Applications

In the realm of algebra, solving equations is a fundamental skill. This article will guide you through the process of solving the equation 0.18 + y = 0.4(7y – 0.9), providing a clear, step-by-step explanation and exploring its real-world relevance.

Understanding the Equation

This equation represents a relationship between two variables: 'y' and a constant. Our goal is to isolate 'y' on one side of the equation to determine its value.

Step-by-Step Solution

1. Distribute: Start by distributing the 0.4 on the right side of the equation:

   0.18 + y = 2.8y - 0.36

2. Combine like terms: Move all terms containing 'y' to one side and constant terms to the other:

   y - 2.8y = -0.36 - 0.18

3. Simplify: Combine the 'y' terms and the constants:

   -1.8y = -0.54

4. Isolate 'y': Divide both sides by -1.8 to solve for 'y':

   y = -0.54 / -1.8

5. Calculate: Perform the division:

   y = 0.3

Therefore, the solution to the equation 0.18 + y = 0.4(7y – 0.9) is y = 0.3.

Real-World Applications

Equations like this find applications in various fields:

• Finance: Imagine you are investing $0.18 in a stock that earns a 10% return. This return is represented by 'y'. The total value of your investment after a certain period is represented by the equation. Solving for 'y' helps you understand the growth of your investment.

• Physics: Equations similar to this are used in calculating the position of an object in motion, where 'y' might represent the displacement of the object.

• Economics: Equations like this can be used in modeling supply and demand, where 'y' might represent the quantity of a product.

In Conclusion

Understanding how to solve algebraic equations like the one we explored is crucial for success in various academic and professional fields. By following the steps outlined above, you can confidently solve such equations and apply them to real-world scenarios.

Note: This article is based on the concepts and explanations found in various resources available on Academia.edu, a platform for sharing academic research. It is important to consult these original sources for further exploration and understanding.