Solve $14 - 3m = 4m$Find $m =$ ___

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Introduction

In this article, we will be solving a linear equation to find the value of the variable m. The equation given is 14 - 3m = 4m. We will use algebraic methods to isolate the variable m and find its value.

Understanding the Equation

The given equation is a linear equation, which means it is an equation in which the highest power of the variable is 1. In this case, the variable is m. The equation is 14 - 3m = 4m. Our goal is to isolate the variable m and find its value.

Isolating the Variable m

To isolate the variable m, we need to get all the terms containing m on one side of the equation and the constant terms on the other side. We can start by adding 3m to both sides of the equation to get rid of the negative term.

14 - 3m + 3m = 4m + 3m
14 = 7m

Solving for m

Now that we have the equation 14 = 7m, we can solve for m by dividing both sides of the equation by 7.

14 / 7 = m
2 = m

Conclusion

In this article, we solved the linear equation 14 - 3m = 4m to find the value of the variable m. We used algebraic methods to isolate the variable m and found its value to be 2.

Final Answer

The final answer is 2\boxed{2}.

Step-by-Step Solution

Here is the step-by-step solution to the problem:

  1. Start with the given equation: 14 - 3m = 4m
  2. Add 3m to both sides of the equation to get rid of the negative term: 14 - 3m + 3m = 4m + 3m
  3. Simplify the equation: 14 = 7m
  4. Divide both sides of the equation by 7 to solve for m: 14 / 7 = m
  5. Simplify the equation: 2 = m

Tips and Tricks

  • When solving linear equations, it's essential to isolate the variable by getting all the terms containing the variable on one side of the equation and the constant terms on the other side.
  • Use algebraic methods such as addition, subtraction, multiplication, and division to isolate the variable.
  • Check your solution by plugging it back into the original equation to ensure that it's true.

Common Mistakes

  • Failing to isolate the variable by not getting all the terms containing the variable on one side of the equation.
  • Not checking the solution by plugging it back into the original equation.
  • Making arithmetic errors when simplifying the equation.

Real-World Applications

  • Solving linear equations is a fundamental skill in mathematics and has numerous real-world applications in fields such as physics, engineering, and economics.
  • Linear equations are used to model real-world situations such as motion, optimization, and decision-making.
  • Understanding how to solve linear equations is essential for problem-solving and critical thinking.

Further Reading

  • For more information on solving linear equations, check out the following resources:
  • Khan Academy: Solving Linear Equations
  • Mathway: Solving Linear Equations
  • MIT OpenCourseWare: Linear Algebra

Conclusion

In conclusion, solving linear equations is a fundamental skill in mathematics that has numerous real-world applications. By following the step-by-step solution outlined in this article, you can solve linear equations and find the value of the variable m. Remember to isolate the variable by getting all the terms containing the variable on one side of the equation and the constant terms on the other side.

Introduction

In our previous article, we solved the linear equation 14 - 3m = 4m to find the value of the variable m. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation in which the variable is not raised to a power greater than 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by getting all the terms containing the variable on one side of the equation and the constant terms on the other side. You can use algebraic methods such as addition, subtraction, multiplication, and division to isolate the variable.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. In other words, a linear equation is a simple equation, while a quadratic equation is a more complex equation.

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

A: Yes, you can use a calculator to solve a linear equation. However, it's essential to understand the steps involved in solving the equation, so you can check your solution and make sure it's correct.

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 by not getting all the terms containing the variable on one side of the equation.
  • Not checking the solution by plugging it back into the original equation.
  • Making arithmetic errors when simplifying the equation.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug it back into the original equation and make sure it's true. If the solution is not true, you need to go back and recheck your work.

Q: Can I use algebraic methods to solve a linear equation with fractions?

A: Yes, you can use algebraic methods to solve a linear equation with fractions. However, you need to be careful when simplifying the equation to avoid making arithmetic errors.

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

A: Solving linear equations has numerous real-world applications in fields such as physics, engineering, and economics. Some examples include:

  • Modeling motion and velocity
  • Optimizing production and cost
  • Making decisions based on data

Q: How do I know if a linear equation has a solution?

A: A linear equation has a solution if it is consistent, meaning that the equation is true for at least one value of the variable. If the equation is inconsistent, meaning that it is not true for any value of the variable, then it has no solution.

Q: Can I use algebraic methods to solve a linear equation with multiple variables?

A: Yes, you can use algebraic methods to solve a linear equation with multiple variables. However, you need to be careful when isolating the variables and making sure that the equation is consistent.

Q: What are some tips for solving linear equations?

A: Some tips for solving linear equations include:

  • Read the equation carefully and make sure you understand what it's asking for.
  • Use algebraic methods to isolate the variable.
  • Check your solution by plugging it back into the original equation.
  • Be careful when simplifying the equation to avoid making arithmetic errors.

Conclusion

In conclusion, solving linear equations is a fundamental skill in mathematics that has numerous real-world applications. By following the tips and tricks outlined in this article, you can solve linear equations and find the value of the variable. Remember to isolate the variable by getting all the terms containing the variable on one side of the equation and the constant terms on the other side.