The Equation and the Proposed Solution

Oct 13, 2025 by pynkocean.com 26 views

Introduction

In mathematics, solving linear equations is a fundamental concept that helps us understand the relationship between variables. In this article, we will focus on verifying a given solution to a linear equation. We will use the equation $1.4n + 2 = 2n + 3.2$ and the proposed solution $n = -2$ to demonstrate the step-by-step process of justification.

The Equation and the Proposed Solution

The given equation is $1.4n + 2 = 2n + 3.2$ . We are asked to verify whether the solution $n = -2$ satisfies this equation. To do this, we need to substitute the value of $n$ into the equation and check if the resulting statement is true.

Step 1: Substitute the Value of n

We will start by substituting $n = -2$ into the equation $1.4n + 2 = 2n + 3.2$ . This gives us:

$1.4(-2) + 2 = 2(-2) + 3.2$

Step 2: Simplify the Equation

Now, we will simplify the equation by performing the arithmetic operations.

$-2.8 + 2 = -4 + 3.2$

Step 3: Combine Like Terms

Next, we will combine like terms to further simplify the equation.

$-0.8 = -0.8$

Conclusion

In this article, we verified the solution $n = -2$ to the equation $1.4n + 2 = 2n + 3.2$ . We did this by substituting the value of $n$ into the equation, simplifying the resulting statement, and combining like terms. The final justification is that $-0.8 = -0.8$ , which confirms that the solution $n = -2$ is indeed a solution to the equation.

The Final Answer

The last line of the justification is:

$-0.8 = -0.8$

This confirms that the solution $n = -2$ is a valid solution to the equation $1.4n + 2 = 2n + 3.2$ .

Answer Options

A. $0.8 = 0.8$ B. $-0.8 = -0.8$ C. $3 = 3$ D. $-3 = -3$

The correct answer is:

Introduction

In our previous article, we demonstrated how to verify a solution to a linear equation using the equation $1.4n + 2 = 2n + 3.2$ and the proposed solution $n = -2$ . In this article, we will address some common questions and concerns that readers may have about verifying solutions to linear equations.

Q: What is the purpose of verifying a solution to a linear equation?

A: The purpose of verifying a solution to a linear equation is to confirm that the proposed solution satisfies the equation. This is an important step in solving linear equations, as it ensures that the solution is correct and accurate.

Q: How do I know if a solution is valid or not?

A: To determine if a solution is valid, you need to substitute the value of the variable into the equation and check if the resulting statement is true. If the statement is true, then the solution is valid. If the statement is false, then the solution is not valid.

Q: What if I get a false statement when I substitute the value of the variable into the equation?

A: If you get a false statement when you substitute the value of the variable into the equation, then the solution is not valid. In this case, you need to re-evaluate the equation and try to find a different solution.

Q: Can I use any method to verify a solution to a linear equation?

A: Yes, you can use any method to verify a solution to a linear equation. However, the most common method is to substitute the value of the variable into the equation and check if the resulting statement is true.

Q: What if I'm not sure if a solution is valid or not?

A: If you're not sure if a solution is valid or not, then it's always best to err on the side of caution and re-evaluate the equation. You can also try using different methods to verify the solution, such as graphing or using a calculator.

Q: Can I use a calculator to verify a solution to a linear equation?

A: Yes, you can use a calculator to verify a solution to a linear equation. However, it's always best to understand the underlying math and to use a calculator as a tool to check your work.

Q: What if I'm still having trouble verifying a solution to a linear equation?

A: If you're still having trouble verifying a solution to a linear equation, then it may be helpful to seek help from a teacher, tutor, or classmate. You can also try watching video tutorials or online lessons to help you understand the concept better.

Conclusion

Verifying solutions to linear equations is an important step in solving linear equations. By understanding the concept and using the right methods, you can confidently verify solutions and ensure that your answers are accurate and correct.

Common Mistakes to Avoid

Not substituting the value of the variable into the equation
Not checking if the resulting statement is true
Not using a calculator to check your work
Not seeking help when needed

Tips and Tricks

Always read the equation carefully and understand what it's asking for
Use a calculator to check your work, but also understand the underlying math
Don't be afraid to ask for help when you're stuck
Practice, practice, practice to become more confident in verifying solutions to linear equations.