Determining The ErrorAshley Solved The Equation For $m$ Using The Following Steps:$\[ \begin{array}{l} -4.5 + M = 17 \\ -4.5 \quad -4.5 \\ m = 12.5 \end{array} \\]What Was Ashley's Error?A. Ashley Should Have Subtracted 17 From Both

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Introduction

Solving equations is a fundamental concept in mathematics, and it requires careful attention to detail to arrive at the correct solution. In this article, we will analyze the steps taken by Ashley to solve an equation and determine the error in her solution.

The Equation

The equation Ashley attempted to solve is:

−4.5+m=17-4.5 + m = 17

Ashley's Solution Steps

Ashley's solution steps are as follows:

${ \begin{array}{l} -4.5 + m = 17 \\ -4.5 \quad -4.5 \\ m = 12.5 \end{array} \}$

Identifying the Error

At first glance, it appears that Ashley's solution is correct. However, upon closer inspection, we can see that there is an error in her solution. The error lies in the second step, where Ashley subtracts 4.5 from both sides of the equation.

Correcting the Error

To correct the error, we need to add 4.5 to both sides of the equation, not subtract it. This is because we are trying to isolate the variable mm, and adding 4.5 to both sides will allow us to do so.

Correct Solution Steps

The correct solution steps are as follows:

${ \begin{array}{l} -4.5 + m = 17 \\ \textbf{Add 4.5 to both sides:} \\ m = 17 + 4.5 \\ m = 21.5 \end{array} \}$

Conclusion

In conclusion, Ashley's error was in subtracting 4.5 from both sides of the equation instead of adding it. This resulted in an incorrect solution of m=12.5m = 12.5. The correct solution is m=21.5m = 21.5, which can be obtained by adding 4.5 to both sides of the equation.

Common Errors in Equation Solving

There are several common errors that students make when solving equations. Some of these errors include:

  • Adding or subtracting the wrong value: This is the error that Ashley made in the example above. Instead of adding 4.5 to both sides, she subtracted it.
  • Not isolating the variable: This is another common error that students make. Instead of isolating the variable, they may end up with an expression that contains multiple variables.
  • Not checking the solution: This is a critical step in solving equations. Students should always check their solution to make sure it is correct.

Tips for Solving Equations

Here are some tips for solving equations:

  • Read the equation carefully: Before starting to solve the equation, read it carefully to make sure you understand what is being asked.
  • Use inverse operations: To solve an equation, you need to use inverse operations to isolate the variable.
  • Check your solution: Always check your solution to make sure it is correct.

Conclusion

Solving equations is a critical skill in mathematics, and it requires careful attention to detail to arrive at the correct solution. By identifying common errors and following tips for solving equations, students can improve their skills and become more confident in their ability to solve equations.

Final Thoughts

In conclusion, solving equations is a complex process that requires careful attention to detail. By understanding the common errors that students make and following tips for solving equations, students can improve their skills and become more confident in their ability to solve equations.

References

  • [1] "Algebra" by Michael Artin
  • [2] "Mathematics for Dummies" by Mary Jane Sterling

Additional Resources

For additional resources on solving equations, please see the following:

  • [1] Khan Academy: Solving Equations
  • [2] Mathway: Solving Equations
  • [3] Wolfram Alpha: Solving Equations
    Frequently Asked Questions (FAQs) About Determining the Error in Ashley's Equation Solution =====================================================================================

Q: What was Ashley's error in solving the equation?

A: Ashley's error was in subtracting 4.5 from both sides of the equation instead of adding it. This resulted in an incorrect solution of m=12.5m = 12.5.

Q: What is the correct solution to the equation?

A: The correct solution to the equation is m=21.5m = 21.5, which can be obtained by adding 4.5 to both sides of the equation.

Q: What are some common errors that students make when solving equations?

A: Some common errors that students make when solving equations include:

  • Adding or subtracting the wrong value: This is the error that Ashley made in the example above. Instead of adding 4.5 to both sides, she subtracted it.
  • Not isolating the variable: This is another common error that students make. Instead of isolating the variable, they may end up with an expression that contains multiple variables.
  • Not checking the solution: This is a critical step in solving equations. Students should always check their solution to make sure it is correct.

Q: How can I avoid making these common errors when solving equations?

A: To avoid making these common errors, follow these tips:

  • Read the equation carefully: Before starting to solve the equation, read it carefully to make sure you understand what is being asked.
  • Use inverse operations: To solve an equation, you need to use inverse operations to isolate the variable.
  • Check your solution: Always check your solution to make sure it is correct.

Q: What are some tips for solving equations?

A: Here are some additional tips for solving equations:

  • Use a systematic approach: When solving an equation, use a systematic approach to isolate the variable.
  • Check your work: Always check your work to make sure you have not made any mistakes.
  • Use a calculator: If you are having trouble solving an equation, try using a calculator to check your work.

Q: How can I practice solving equations?

A: There are many ways to practice solving equations, including:

  • Working through practice problems: Try working through practice problems to help you build your skills.
  • Using online resources: There are many online resources available that can help you practice solving equations.
  • Seeking help from a teacher or tutor: If you are having trouble solving equations, don't be afraid to seek help from a teacher or tutor.

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

A: Solving equations has many real-world applications, including:

  • Science and engineering: Solving equations is used in many scientific and engineering applications, such as calculating the trajectory of a projectile or the stress on a beam.
  • Finance: Solving equations is used in finance to calculate interest rates and investment returns.
  • Computer science: Solving equations is used in computer science to solve problems in fields such as machine learning and data analysis.

Q: How can I improve my skills in solving equations?

A: To improve your skills in solving equations, try the following:

  • Practice regularly: The more you practice solving equations, the better you will become.
  • Seek help from a teacher or tutor: If you are having trouble solving equations, don't be afraid to seek help from a teacher or tutor.
  • Use online resources: There are many online resources available that can help you practice solving equations.

Conclusion

Solving equations is a critical skill in mathematics, and it requires careful attention to detail to arrive at the correct solution. By understanding the common errors that students make and following tips for solving equations, students can improve their skills and become more confident in their ability to solve equations.