Importance of Checking Work

Oct 13, 2025 by pynkocean.com 74 views

Introduction

Solving equations is a fundamental concept in mathematics, and it requires a deep understanding of algebraic manipulations. However, even the most skilled mathematicians can make mistakes when solving equations. In this article, we will examine a step-by-step solution to an equation and identify the mistake made in the process.

The Equation

The equation given is:

6x - 1 = -2x + 9

Step-by-Step Solution

The solution provided is as follows:

\begin{aligned} 6x - 1 & = -2x + 9 \\ 8x - 1 & = 9 \\ 8x & = 10 \\ x & = \frac{8}{10} \\ x & = \frac{4}{5} \end{aligned}

Identifying the Mistake

Let's examine the solution step by step to identify the mistake.

Step 1: Adding 1 to Both Sides

The first step is to add 1 to both sides of the equation:

6x - 1 + 1 = -2x + 9 + 1

This simplifies to:

6x = -2x + 10

Step 2: Adding 2x to Both Sides

The next step is to add 2x to both sides of the equation:

6x + 2x = -2x + 2x + 10

This simplifies to:

8x = 10

Step 3: Dividing Both Sides by 8

The final step is to divide both sides of the equation by 8:

\frac{8x}{8} = \frac{10}{8}

This simplifies to:

x = \frac{5}{4}

The Mistake

The mistake in the original solution is in the third step, where it is stated that:

8x = 10

This is incorrect, as the correct solution is:

x = \frac{5}{4}

The original solution incorrectly states that:

x = \frac{8}{10}

which is equivalent to:

x = \frac{4}{5}

Conclusion

In conclusion, the mistake in the original solution is in the third step, where it is stated that:

8x = 10

This is incorrect, and the correct solution is:

x = \frac{5}{4}

Importance of Checking Work

This example highlights the importance of checking work when solving equations. Even the most skilled mathematicians can make mistakes, and it is essential to double-check the solution to ensure that it is correct.

Tips for Solving Equations

Here are some tips for solving equations:

Read the problem carefully: Before starting to solve the equation, read the problem carefully to ensure that you understand what is being asked.
Use algebraic manipulations: Algebraic manipulations, such as adding, subtracting, multiplying, and dividing both sides of the equation, can help to simplify the equation and solve for the variable.
Check your work: Once you have solved the equation, check your work to ensure that it is correct.
Use a calculator: If you are unsure about the solution, use a calculator to check your work.

Common Mistakes in Solving Equations

Here are some common mistakes to avoid when solving equations:

Not reading the problem carefully: Failing to read the problem carefully can lead to misunderstandings and incorrect solutions.
Not using algebraic manipulations: Failing to use algebraic manipulations can make it difficult to simplify the equation and solve for the variable.
Not checking work: Failing to check work can lead to incorrect solutions.
Not using a calculator: Failing to use a calculator can make it difficult to check work and ensure that the solution is correct.

Conclusion

Introduction

Solving equations is a fundamental concept in mathematics, and it requires a deep understanding of algebraic manipulations. In our previous article, we examined a step-by-step solution to an equation and identified the mistake made in the process. In this article, we will provide a Q&A guide to help you better understand how to solve equations.

Q: What is an equation?

A: An equation is a statement that two mathematical expressions are equal. It is a way of expressing a relationship between two or more variables.

Q: What are the basic steps to solve an equation?

A: The basic steps to solve an equation are:

Read the problem carefully: Before starting to solve the equation, read the problem carefully to ensure that you understand what is being asked.
Use algebraic manipulations: Algebraic manipulations, such as adding, subtracting, multiplying, and dividing both sides of the equation, can help to simplify the equation and solve for the variable.
Check your work: Once you have solved the equation, check your work to ensure that it is correct.
Use a calculator: If you are unsure about the solution, use a calculator to check your work.

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

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

Not reading the problem carefully: Failing to read the problem carefully can lead to misunderstandings and incorrect solutions.
Not using algebraic manipulations: Failing to use algebraic manipulations can make it difficult to simplify the equation and solve for the variable.
Not checking work: Failing to check work can lead to incorrect solutions.
Not using a calculator: Failing to use a calculator can make it difficult to check work and ensure that the solution is correct.

Q: How do I know if I have solved the equation correctly?

A: To ensure that you have solved the equation correctly, follow these steps:

Check your work: Once you have solved the equation, check your work to ensure that it is correct.
Use a calculator: If you are unsure about the solution, use a calculator to check your work.
Get help: If you are still unsure about the solution, ask a teacher or tutor for help.

Q: What are some tips for solving equations?

A: Here are some tips for solving equations:

Use algebraic manipulations: Algebraic manipulations, such as adding, subtracting, multiplying, and dividing both sides of the equation, can help to simplify the equation and solve for the variable.
Check your work: Once you have solved the equation, check your work to ensure that it is correct.
Use a calculator: If you are unsure about the solution, use a calculator to check your work.
Get help: If you are still unsure about the solution, ask a teacher or tutor for help.

Q: How do I handle equations with variables on both sides?

A: To handle equations with variables on both sides, follow these steps:

Add or subtract the same value to both sides: Add or subtract the same value to both sides of the equation to eliminate the variable on one side.
Multiply or divide both sides by the same value: Multiply or divide both sides of the equation by the same value to eliminate the variable on one side.
Check your work: Once you have solved the equation, check your work to ensure that it is correct.

Q: How do I handle equations with fractions?

A: To handle equations with fractions, follow these steps:

Multiply both sides by the least common multiple (LCM): Multiply both sides of the equation by the LCM to eliminate the fractions.
Check your work: Once you have solved the equation, check your work to ensure that it is correct.

Conclusion

In conclusion, solving equations requires a deep understanding of algebraic manipulations and attention to detail. By following the tips and avoiding common mistakes, you can ensure that your solutions are correct and accurate. Remember to read the problem carefully, use algebraic manipulations, check your work, and use a calculator to check your work. If you are still unsure about the solution, ask a teacher or tutor for help.