Solve The Equation 0.45x +0.3 + 0.20x = 8

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, 0.45x + 0.3 + 0.20x = 8, using a step-by-step approach. We will break down the equation into manageable parts, apply the necessary operations, and arrive at the solution.

Understanding the Equation

The given equation is a linear equation in one variable, x. It consists of three terms: 0.45x, 0.3, and 0.20x, which are added together to equal 8. To solve for x, we need to isolate the variable x on one side of the equation.

Step 1: Combine Like Terms

The first step in solving the equation is to combine the like terms, which are the terms that contain the variable x. In this case, the like terms are 0.45x and 0.20x.

# Combine like terms
equation = "0.45x + 0.20x"
combined_terms = "0.65x"

By combining the like terms, we get 0.65x.

Step 2: Simplify the Equation

Now that we have combined the like terms, we can simplify the equation by subtracting 0.3 from both sides.

# Simplify the equation
equation = "0.65x + 0.3 = 8"
simplified_equation = "0.65x = 8 - 0.3"

By subtracting 0.3 from both sides, we get 0.65x = 7.7.

Step 3: Solve for x

Now that we have simplified the equation, we can solve for x by dividing both sides by 0.65.

# Solve for x
equation = "0.65x = 7.7"
solution = "x = 7.7 / 0.65"

By dividing both sides by 0.65, we get x = 11.846.

Conclusion

In this article, we solved the linear equation 0.45x + 0.3 + 0.20x = 8 using a step-by-step approach. We combined like terms, simplified the equation, and solved for x. The solution to the equation is x = 11.846.

Tips and Tricks

  • When solving linear equations, it's essential to combine like terms and simplify the equation to make it easier to solve.
  • When dividing both sides of an equation by a coefficient, make sure to check if the coefficient is zero to avoid division by zero errors.
  • When solving linear equations, it's essential to check the solution by plugging it back into the original equation to ensure that it's true.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Finance: Linear equations are used to calculate interest rates, investment returns, and loan payments.
  • Science: Linear equations are used to model population growth, chemical reactions, and physical systems.
  • Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Common Mistakes

  • When solving linear equations, it's easy to make mistakes by forgetting to combine like terms or simplify the equation.
  • When dividing both sides of an equation by a coefficient, it's easy to make mistakes by forgetting to check if the coefficient is zero.
  • When solving linear equations, it's essential to check the solution by plugging it back into the original equation to ensure that it's true.

Conclusion

In conclusion, solving linear equations is a crucial skill for students and professionals alike. By following a step-by-step approach, combining like terms, simplifying the equation, and solving for x, we can arrive at the solution to the equation. Remember to check the solution by plugging it back into the original equation to ensure that it's true.