Solve The Following Equation. Show All Your Work.${ 21.3 = X + 5.1 }$

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, step by step, to help readers understand the process and build their confidence in solving similar equations.

The Equation

The given equation is:

21.3=x+5.1{ 21.3 = x + 5.1 }

Our goal is to isolate the variable x and find its value.

Step 1: Subtract 5.1 from Both Sides

To start solving the equation, we need to get rid of the constant term on the right-hand side. We can do this by subtracting 5.1 from both sides of the equation.

21.3−5.1=x+5.1−5.1{ 21.3 - 5.1 = x + 5.1 - 5.1 }

This simplifies to:

16.2=x{ 16.2 = x }

Step 2: Check the Solution

To ensure that our solution is correct, we can plug it back into the original equation and check if it holds true.

21.3=16.2+5.1{ 21.3 = 16.2 + 5.1 }

21.3=21.3{ 21.3 = 21.3 }

Since the equation holds true, our solution is correct.

Conclusion

Solving linear equations is a straightforward process that requires careful attention to detail. By following the steps outlined in this article, readers should be able to solve similar equations with ease. Remember to always check your solution to ensure that it is correct.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS).
  • Make sure to isolate the variable on one side of the equation.
  • Check your solution by plugging it back into the original equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Finance: Calculating interest rates and investment returns.
  • Science: Modeling population growth and chemical reactions.
  • Engineering: Designing bridges and buildings.

Common Mistakes

  • Failing to isolate the variable on one side of the equation.
  • Not checking the solution.
  • Not following the order of operations (PEMDAS).

Final Thoughts

Solving linear equations is a fundamental skill that is essential for success in mathematics and other fields. By following the steps outlined in this article and practicing regularly, readers should be able to solve linear equations with ease.

Additional Resources

For more information on solving linear equations, check out the following resources:

  • Khan Academy: Linear Equations
  • Mathway: Solving Linear Equations
  • Wolfram Alpha: Linear Equations

Frequently Asked Questions

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.

Q: How do I solve a linear equation? A: To solve a linear equation, follow the steps outlined in this article.

Q: What are some common mistakes to avoid when solving linear equations? A: Failing to isolate the variable on one side of the equation, not checking the solution, and not following the order of operations (PEMDAS).

Conclusion

Solving linear equations is a straightforward process that requires careful attention to detail. By following the steps outlined in this article and practicing regularly, readers should be able to solve linear equations with ease. Remember to always check your solution to ensure that it is correct.

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Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that practice makes perfect, and sometimes, it's helpful to have a refresher on the concepts. In this article, we'll answer some frequently asked questions about solving linear equations, providing you with a deeper understanding of the subject.

Q&A

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow these steps:

  1. Isolate the variable on one side of the equation.
  2. Use inverse operations to get rid of the constant term.
  3. Check your solution by plugging it back into the original equation.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Failing to isolate the variable on one side of the equation.
  • Not checking the solution.
  • Not following the order of operations (PEMDAS).

Q: How do I handle equations with fractions?

A: When solving equations with fractions, follow these steps:

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
  2. Simplify the equation.
  3. Solve for the variable.

Q: How do I handle equations with decimals?

A: When solving equations with decimals, follow these steps:

  1. Multiply both sides of the equation by a power of 10 to eliminate the decimals.
  2. Simplify the equation.
  3. Solve for the variable.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, make sure to check your solution by plugging it back into the original equation to ensure that it is correct.

Q: How do I graph linear equations?

A: To graph a linear equation, follow these steps:

  1. Find two points on the line.
  2. Plot the points on a coordinate plane.
  3. Draw a line through the points.

Q: What are some real-world applications of linear equations?

A: Linear equations have numerous real-world applications, including:

  • Finance: Calculating interest rates and investment returns.
  • Science: Modeling population growth and chemical reactions.
  • Engineering: Designing bridges and buildings.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS).
  • Make sure to isolate the variable on one side of the equation.
  • Check your solution by plugging it back into the original equation.

Common Misconceptions

  • Many people believe that linear equations are only used in mathematics. However, they have numerous real-world applications.
  • Some people think that solving linear equations is difficult. However, with practice, it becomes second nature.

Conclusion

Solving linear equations is a fundamental skill that is essential for success in mathematics and other fields. By following the steps outlined in this article and practicing regularly, you should be able to solve linear equations with ease. Remember to always check your solution to ensure that it is correct.

Additional Resources

For more information on solving linear equations, check out the following resources:

  • Khan Academy: Linear Equations
  • Mathway: Solving Linear Equations
  • Wolfram Alpha: Linear Equations

Frequently Asked Questions

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.

Q: How do I solve a linear equation? A: To solve a linear equation, follow the steps outlined in this article.

Q: What are some common mistakes to avoid when solving linear equations? A: Failing to isolate the variable on one side of the equation, not checking the solution, and not following the order of operations (PEMDAS).

Final Thoughts

Solving linear equations is a fundamental skill that is essential for success in mathematics and other fields. By following the steps outlined in this article and practicing regularly, you should be able to solve linear equations with ease. Remember to always check your solution to ensure that it is correct.