Solve For { U $} : : : { 7 - 6u = 5u + 29 \}

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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, 7 - 6u = 5u + 29, and provide a step-by-step guide on how to approach it.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Given Equation

The given equation is 7 - 6u = 5u + 29. This equation is a linear equation in one variable, u. Our goal is to solve for u, which means we need to isolate u on one side of the equation.

Step 1: Simplify the Equation

To simplify the equation, we can start by combining like terms. In this case, we can combine the terms involving u.

7 - 6u = 5u + 29

We can rewrite the equation as:

7 - 6u - 5u = 29

This simplifies to:

7 - 11u = 29

Step 2: Isolate the Variable

Now that we have simplified the equation, we can isolate the variable u. To do this, we need to get rid of the constant term on the same side as u. We can do this by subtracting 7 from both sides of the equation.

7 - 11u = 29
-7 - 11u = -29

This simplifies to:

-11u = -36

Step 3: Solve for the Variable

Now that we have isolated the variable u, we can solve for it. To do this, we need to get rid of the coefficient of u, which is -11. We can do this by dividing both sides of the equation by -11.

-11u = -36
u = -36 / -11

This simplifies to:

u = 36/11

Conclusion

In this article, we have solved a linear equation, 7 - 6u = 5u + 29, using a step-by-step approach. We simplified the equation, isolated the variable, and solved for it. The solution to the equation is u = 36/11. This demonstrates the importance of following a systematic approach when solving linear equations.

Tips and Tricks

When solving linear equations, it is essential to follow a systematic approach. Here are some tips and tricks to keep in mind:

  • Simplify the equation: Combine like terms and simplify the equation as much as possible.
  • Isolate the variable: Get rid of the constant term on the same side as the variable.
  • Use inverse operations: Use inverse operations, such as addition and subtraction, to isolate the variable.
  • Check your solution: Check your solution by plugging it back into the original equation.

By following these tips and tricks, you can become proficient in solving linear equations and tackle more complex problems with confidence.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects, including velocity and acceleration.
  • Engineering: Linear equations are used to design and optimize systems, including electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems, including supply and demand.

In conclusion, solving linear equations is a crucial skill that has numerous real-world applications. By following a systematic approach and using inverse operations, you can solve linear equations with confidence and tackle more complex problems with ease.

Additional Resources

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

  • Mathway: A math problem solver that can help you solve linear equations and other math problems.
  • Khan Academy: A free online resource that provides video lessons and practice exercises on solving linear equations.
  • MIT OpenCourseWare: A free online resource that provides lecture notes and practice exercises on solving linear equations.

Introduction

In our previous article, we discussed how to solve linear equations using a step-by-step approach. In this article, we will provide a Q&A guide to help you understand and apply the concepts of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that 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 simplify a linear equation?

A: To simplify a linear equation, you can combine like terms and simplify the equation as much as possible. This involves adding or subtracting the same value to both sides of the equation.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, you need to get rid of the constant term on the same side as the variable. This can be done by adding or subtracting the same value to both sides of the equation.

Q: What is the inverse operation of addition?

A: The inverse operation of addition is subtraction. This means that if you add a value to both sides of an equation, you can subtract the same value from both sides to isolate the variable.

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 verify that it is true. This ensures that your solution is correct and accurate.

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

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

  • Not simplifying the equation: Failing to simplify the equation can make it difficult to isolate the variable.
  • Not using inverse operations: Failing to use inverse operations can make it difficult to isolate the variable.
  • Not checking the solution: Failing to check the solution can lead to incorrect answers.

Q: How do I apply linear equations to real-world problems?

A: Linear equations can be applied to a wide range of real-world problems, including:

  • Physics: Linear equations are used to describe the motion of objects, including velocity and acceleration.
  • Engineering: Linear equations are used to design and optimize systems, including electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems, including supply and demand.

Q: What are some resources available to help me learn more about solving linear equations?

A: Some resources available to help you learn more about solving linear equations include:

  • Mathway: A math problem solver that can help you solve linear equations and other math problems.
  • Khan Academy: A free online resource that provides video lessons and practice exercises on solving linear equations.
  • MIT OpenCourseWare: A free online resource that provides lecture notes and practice exercises on solving linear equations.

Conclusion

Solving linear equations is a crucial skill that has numerous real-world applications. By following a systematic approach and using inverse operations, you can solve linear equations with confidence and tackle more complex problems with ease. We hope this Q&A guide has provided you with a better understanding of solving linear equations and has helped you to apply the concepts to real-world problems.

Additional Resources

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

  • Mathway: A math problem solver that can help you solve linear equations and other math problems.
  • Khan Academy: A free online resource that provides video lessons and practice exercises on solving linear equations.
  • MIT OpenCourseWare: A free online resource that provides lecture notes and practice exercises on solving linear equations.

By following these resources and practicing regularly, you can become proficient in solving linear equations and tackle more complex problems with confidence.