Clara Solved The Equation 7 3 X = − 2 3 \frac{7}{3} X = -\frac{2}{3} 3 7 ​ X = − 3 2 ​ As Shown:${ \begin{aligned} \frac{7}{3} \times \left(\frac{3}{7}\right) & = -\frac{2}{3} \times \left(\frac{3}{7}\right) \ x & = -14 \end{aligned} }$What Is Clara's Error?A.

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Introduction

Solving equations is a fundamental concept in mathematics, and it requires careful attention to detail. In this article, we will examine Clara's solution to the equation 73x=−23\frac{7}{3} x = -\frac{2}{3} and identify her error. We will also provide a step-by-step solution to the equation and discuss the importance of following the correct order of operations.

Clara's Solution

Clara's solution to the equation is shown below:

{ \begin{aligned} \frac{7}{3} \times \left(\frac{3}{7}\right) & = -\frac{2}{3} \times \left(\frac{3}{7}\right) \\ x & = -14 \end{aligned} \}

Error Analysis

At first glance, Clara's solution appears to be correct. However, upon closer inspection, we can see that she made a mistake. The error lies in the fact that she multiplied both sides of the equation by 37\frac{3}{7}, which is the reciprocal of 73\frac{7}{3}. This is incorrect because it changes the value of the equation.

Correct Solution

To solve the equation correctly, we need to isolate the variable xx by multiplying both sides of the equation by the reciprocal of 73\frac{7}{3}, which is 37\frac{3}{7}. However, we should multiply both sides by 37\frac{3}{7} and then divide both sides by 73\frac{7}{3} to get the correct solution.

{ \begin{aligned} \frac{7}{3} x & = -\frac{2}{3} \\ \frac{3}{7} \times \left(\frac{7}{3} x\right) & = \frac{3}{7} \times \left(-\frac{2}{3}\right) \\ x & = -\frac{2}{7} \end{aligned} \}

Discussion

Clara's error in solving the equation is a common mistake that many students make. It is essential to follow the correct order of operations and to be careful when multiplying and dividing fractions. In this case, Clara multiplied both sides of the equation by the reciprocal of 73\frac{7}{3}, which changed the value of the equation.

Conclusion

In conclusion, Clara's error in solving the equation 73x=−23\frac{7}{3} x = -\frac{2}{3} was due to her incorrect multiplication of both sides of the equation by the reciprocal of 73\frac{7}{3}. The correct solution to the equation is x=−27x = -\frac{2}{7}. It is essential to follow the correct order of operations and to be careful when multiplying and dividing fractions to avoid making similar mistakes.

Importance of Following the Correct Order of Operations

Following the correct order of operations is crucial when solving equations. It ensures that the equation is solved correctly and that the solution is accurate. In this case, Clara's failure to follow the correct order of operations led to an incorrect solution.

Common Mistakes in Solving Equations

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

  • Incorrect multiplication or division of fractions: This is a common mistake that many students make. It is essential to be careful when multiplying and dividing fractions to avoid making similar mistakes.
  • Failure to follow the correct order of operations: Following the correct order of operations is crucial when solving equations. It ensures that the equation is solved correctly and that the solution is accurate.
  • Incorrect simplification of fractions: Simplifying fractions is an essential step in solving equations. It is crucial to simplify fractions correctly to avoid making similar mistakes.

Tips for Solving Equations

Solving equations can be challenging, but there are several tips that can help. Some of these tips include:

  • Read the equation carefully: Before solving the equation, it is essential to read it carefully and understand what is being asked.
  • Follow the correct order of operations: Following the correct order of operations is crucial when solving equations. It ensures that the equation is solved correctly and that the solution is accurate.
  • Be careful when multiplying and dividing fractions: Multiplying and dividing fractions can be challenging, but it is essential to be careful to avoid making similar mistakes.
  • Simplify fractions correctly: Simplifying fractions is an essential step in solving equations. It is crucial to simplify fractions correctly to avoid making similar mistakes.

Conclusion

Introduction

In our previous article, we examined Clara's solution to the equation 73x=−23\frac{7}{3} x = -\frac{2}{3} and identified her error. We also provided a step-by-step solution to the equation and discussed the importance of following the correct order of operations. In this article, we will answer some frequently asked questions about Clara's error and provide additional tips for solving equations.

Q: What is the correct solution to the equation 73x=−23\frac{7}{3} x = -\frac{2}{3}?

A: The correct solution to the equation is x=−27x = -\frac{2}{7}.

Q: Why did Clara make a mistake in solving the equation?

A: Clara made a mistake in solving the equation because she multiplied both sides of the equation by the reciprocal of 73\frac{7}{3}, which changed the value of the equation.

Q: What is the importance of following the correct order of operations?

A: Following the correct order of operations is crucial when solving equations. It ensures that the equation is solved correctly and that the solution is accurate.

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

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

  • Incorrect multiplication or division of fractions: This is a common mistake that many students make. It is essential to be careful when multiplying and dividing fractions to avoid making similar mistakes.
  • Failure to follow the correct order of operations: Following the correct order of operations is crucial when solving equations. It ensures that the equation is solved correctly and that the solution is accurate.
  • Incorrect simplification of fractions: Simplifying fractions is an essential step in solving equations. It is crucial to simplify fractions correctly to avoid making similar mistakes.

Q: How can I avoid making similar mistakes when solving equations?

A: To avoid making similar mistakes when solving equations, it is essential to:

  • Read the equation carefully: Before solving the equation, it is essential to read it carefully and understand what is being asked.
  • Follow the correct order of operations: Following the correct order of operations is crucial when solving equations. It ensures that the equation is solved correctly and that the solution is accurate.
  • Be careful when multiplying and dividing fractions: Multiplying and dividing fractions can be challenging, but it is essential to be careful to avoid making similar mistakes.
  • Simplify fractions correctly: Simplifying fractions is an essential step in solving equations. It is crucial to simplify fractions correctly to avoid making similar mistakes.

Q: What are some tips for solving equations?

A: Some tips for solving equations include:

  • Use the correct order of operations: Following the correct order of operations is crucial when solving equations. It ensures that the equation is solved correctly and that the solution is accurate.
  • Be careful when multiplying and dividing fractions: Multiplying and dividing fractions can be challenging, but it is essential to be careful to avoid making similar mistakes.
  • Simplify fractions correctly: Simplifying fractions is an essential step in solving equations. It is crucial to simplify fractions correctly to avoid making similar mistakes.
  • Check your work: It is essential to check your work when solving equations to ensure that the solution is accurate.

Conclusion

In conclusion, Clara's error in solving the equation 73x=−23\frac{7}{3} x = -\frac{2}{3} was due to her incorrect multiplication of both sides of the equation by the reciprocal of 73\frac{7}{3}. The correct solution to the equation is x=−27x = -\frac{2}{7}. It is essential to follow the correct order of operations and to be careful when multiplying and dividing fractions to avoid making similar mistakes. By following the tips and advice provided in this article, you can avoid making similar mistakes and become a proficient equation solver.