Comparison with Expected Solution

Oct 13, 2025 by windailys.com 97 views

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Introduction

In the world of mathematics, solving equations is a fundamental concept that requires precision and accuracy. Two individuals, Cedric and Insha, were tasked with solving the same equation using their respective calculations. In this article, we will delve into the calculations provided by Insha and analyze the steps taken to arrive at the solution. We will also compare Insha's work with the expected solution to determine the accuracy of her calculations.

Insha's Work

Insha's work on the equation is presented below:

{ \begin{array}{c} \text{Insha's Work} \\ \hline z - 4.5 = -1.5 \\ z - 4.5 + (-4.5) = -1.5 + (-4.5) \\ z = -6 \end{array} \}

Step-by-Step Analysis

Let's break down Insha's work step by step to understand the reasoning behind her calculations.

Step 1: Isolate the Variable

The first step in solving an equation is to isolate the variable. In this case, the variable is z. The equation provided is:

z - 4.5 = -1.5

To isolate z, we need to get rid of the -4.5 on the left-hand side of the equation. This can be done by adding 4.5 to both sides of the equation.

Step 2: Add 4.5 to Both Sides

Adding 4.5 to both sides of the equation gives us:

z - 4.5 + 4.5 = -1.5 + 4.5

This simplifies to:

z = -1.5 + 4.5

Step 3: Simplify the Right-Hand Side

Now, let's simplify the right-hand side of the equation by adding -1.5 and 4.5.

-1.5 + 4.5 = 3

So, the equation becomes:

z = 3

Comparison with Expected Solution

The expected solution to the equation is z = -6. However, Insha's work suggests that z = 3. This indicates that there is an error in Insha's calculations.

Conclusion

In conclusion, Insha's work on the equation is incorrect. The expected solution to the equation is z = -6, but Insha's calculations suggest that z = 3. This highlights the importance of double-checking calculations to ensure accuracy.

Recommendations

To improve the accuracy of their calculations, Cedric and Insha should:

Double-check their work: Before arriving at a solution, double-check each step to ensure that the calculations are correct.
Use a calculator or computer program: Utilize a calculator or computer program to verify the accuracy of their calculations.
Seek help from a teacher or tutor: If unsure about a particular step or calculation, seek help from a teacher or tutor.

By following these recommendations, Cedric and Insha can improve the accuracy of their calculations and arrive at the correct solution to the equation.

Final Thoughts

Solving equations is a fundamental concept in mathematics that requires precision and accuracy. Insha's work on the equation highlights the importance of double-checking calculations to ensure accuracy. By following the recommendations outlined in this article, Cedric and Insha can improve the accuracy of their calculations and arrive at the correct solution to the equation.

Glossary of Terms

Equation: A statement that expresses the equality of two mathematical expressions.
Variable: A symbol or expression that represents a value that can change.
Solution: The value or values that satisfy an equation.

References

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

Additional Resources

Khan Academy: Algebra
Mathway: Algebra Solver
Wolfram Alpha: Algebra Calculator

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Introduction

In our previous article, we analyzed the calculations provided by Insha to solve the equation z - 4.5 = -1.5. We found that Insha's work was incorrect, and the expected solution to the equation is z = -6. In this article, we will address some of the frequently asked questions related to the equation and its solution.

Q&A

Q: What is the correct solution to the equation z - 4.5 = -1.5?

A: The correct solution to the equation z - 4.5 = -1.5 is z = -6.

Q: Why is Insha's work incorrect?

A: Insha's work is incorrect because she added -4.5 to both sides of the equation, which resulted in z = 3. However, the correct solution to the equation is z = -6.

Q: What is the difference between the expected solution and Insha's solution?

A: The expected solution to the equation is z = -6, while Insha's solution is z = 3. This indicates that there is an error in Insha's calculations.

Q: How can I improve my calculations to ensure accuracy?

A: To improve your calculations, you can:

Double-check your work: Before arriving at a solution, double-check each step to ensure that the calculations are correct.
Use a calculator or computer program: Utilize a calculator or computer program to verify the accuracy of your calculations.
Seek help from a teacher or tutor: If unsure about a particular step or calculation, seek help from a teacher or tutor.

Q: What is the importance of double-checking calculations?

A: Double-checking calculations is essential to ensure accuracy. It helps to identify errors and ensures that the solution to the equation is correct.

Q: Can I use a calculator or computer program to solve equations?

A: Yes, you can use a calculator or computer program to solve equations. These tools can help to verify the accuracy of your calculations and provide the correct solution to the equation.

Q: What should I do if I am unsure about a particular step or calculation?

A: If you are unsure about a particular step or calculation, seek help from a teacher or tutor. They can provide guidance and help you to understand the concept.

Conclusion

In conclusion, solving equations requires precision and accuracy. Insha's work on the equation highlights the importance of double-checking calculations to ensure accuracy. By following the recommendations outlined in this article, you can improve the accuracy of your calculations and arrive at the correct solution to the equation.

Glossary of Terms

Equation: A statement that expresses the equality of two mathematical expressions.
Variable: A symbol or expression that represents a value that can change.
Solution: The value or values that satisfy an equation.
Calculator: A tool used to perform mathematical calculations.
Computer program: A set of instructions that can be used to solve mathematical problems.

References

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

Additional Resources

Khan Academy: Algebra
Mathway: Algebra Solver
Wolfram Alpha: Algebra Calculator