Substituting the Solution into the Equation

Oct 13, 2025 by windailys.com 124 views

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Introduction

In this article, we will delve into the solution of a given equation and verify whether the proposed solution is indeed correct. The equation in question is $$1.4n + 2 = 2n + 3.2$$, and we are given that the solution is $$n=-2$$. Our goal is to justify this solution by substituting it back into the original equation and verifying that it satisfies the equation.

Substituting the Solution into the Equation

To verify the solution, we will substitute $$n=-2$$ into the original equation. This involves replacing every instance of $$n$$ with $$-2$$ in the equation.

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

Simplifying the Equation

Now that we have substituted the solution into the equation, we can simplify both sides of the equation to see if they are indeed equal.

-2.8 + 2 = -4 + 3.2

Further Simplification

We can further simplify the equation by combining like terms on both sides.

-2.8 + 2 = -4 + 3.2

-0.8 = -0.8

Conclusion

After simplifying the equation, we can see that the left-hand side and the right-hand side are indeed equal. This confirms that the solution $$n=-2$$ is indeed a solution to the equation $$1.4n + 2 = 2n + 3.2$$.

Justification

The last line of the justification is:

-0.8 = -0.8

This confirms that the solution $$n=-2$$ satisfies the equation, and therefore, it is a valid solution.

Final Answer

Based on the justification provided, the correct answer is:

B. $$-0.8 = -0.8$$

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

Discussion

The solution to the equation $$1.4n + 2 = 2n + 3.2$$ can be verified by substituting the solution $$n=-2$$ into the original equation and simplifying both sides. The final answer is $$-0.8 = -0.8$$, which confirms that the solution $$n=-2$$ is indeed a solution to the equation.

Conclusion

In this article, we verified the solution $$n=-2$$ to the equation $$1.4n + 2 = 2n + 3.2$$ by substituting the solution into the original equation and simplifying both sides. The final answer is $$-0.8 = -0.8$$, which confirms that the solution $$n=-2$$ is indeed a solution to the equation.

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Q: What is the first step in verifying a solution to a linear equation?

A: The first step in verifying a solution to a linear equation is to substitute the proposed solution into the original equation.

Q: Why is it necessary to substitute the solution into the original equation?

A: It is necessary to substitute the solution into the original equation to ensure that the solution satisfies the equation. This involves replacing every instance of the variable with the proposed solution.

Q: What is the next step after substituting the solution into the equation?

A: After substituting the solution into the equation, the next step is to simplify both sides of the equation to see if they are indeed equal.

Q: How do I simplify both sides of the equation?

A: To simplify both sides of the equation, you can combine like terms on both sides. This involves adding or subtracting the same value from both sides of the equation.

Q: What if the left-hand side and the right-hand side of the equation are not equal?

A: If the left-hand side and the right-hand side of the equation are not equal, then the proposed solution is not a solution to the equation.

Q: What is the final step in verifying a solution to a linear equation?

A: The final step in verifying a solution to a linear equation is to confirm that the solution satisfies the equation. This can be done by checking if the left-hand side and the right-hand side of the equation are indeed equal.

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

A: A solution is valid if it satisfies the equation. This can be confirmed by substituting the solution into the original equation and simplifying both sides.

Q: What if I get a true statement after simplifying the equation?

A: If you get a true statement after simplifying the equation, then the proposed solution is indeed a solution to the equation.

Q: Can I use this method to verify solutions to other types of equations?

A: Yes, this method can be used to verify solutions to other types of equations, including quadratic equations and polynomial equations.

Q: Are there any other methods to verify solutions to linear equations?

A: Yes, there are other methods to verify solutions to linear equations, including using a graphing calculator or a computer algebra system.

Q: How do I choose the best method to verify a solution to a linear equation?

A: The best method to verify a solution to a linear equation depends on the specific equation and the tools available. You can choose the method that is most convenient and efficient for you.

Q: Can I use this method to solve linear equations?

A: Yes, this method can be used to solve linear equations. By substituting the solution into the original equation and simplifying both sides, you can find the solution to the equation.

Q: Are there any tips or tricks to help me verify solutions to linear equations?

A: Yes, here are some tips and tricks to help you verify solutions to linear equations:

Make sure to substitute the solution into the original equation carefully.
Simplify both sides of the equation thoroughly.
Check if the left-hand side and the right-hand side of the equation are indeed equal.
Use a graphing calculator or a computer algebra system to verify the solution if possible.

Q: Can I use this method to verify solutions to systems of linear equations?

A: Yes, this method can be used to verify solutions to systems of linear equations. By substituting the solution into the original system of equations and simplifying both sides, you can verify that the solution satisfies the system of equations.

Q: Are there any other resources available to help me verify solutions to linear equations?

A: Yes, there are many resources available to help you verify solutions to linear equations, including online tutorials, videos, and textbooks. You can also ask your teacher or a tutor for help if you need it.

Q: How do I know if a solution is a valid solution to a system of linear equations?

A: A solution is a valid solution to a system of linear equations if it satisfies all the equations in the system. This can be confirmed by substituting the solution into each equation in the system and simplifying both sides.

Q: Can I use this method to verify solutions to nonlinear equations?

A: No, this method is not suitable for verifying solutions to nonlinear equations. Nonlinear equations require different methods and techniques to solve and verify solutions.

Q: Are there any other methods to verify solutions to nonlinear equations?

A: Yes, there are other methods to verify solutions to nonlinear equations, including using numerical methods or approximation techniques.

Q: How do I choose the best method to verify a solution to a nonlinear equation?

A: The best method to verify a solution to a nonlinear equation depends on the specific equation and the tools available. You can choose the method that is most convenient and efficient for you.

Q: Can I use this method to solve nonlinear equations?

A: No, this method is not suitable for solving nonlinear equations. Nonlinear equations require different methods and techniques to solve.

Q: Are there any tips or tricks to help me verify solutions to nonlinear equations?

A: Yes, here are some tips and tricks to help you verify solutions to nonlinear equations:

Make sure to use the correct method and technique for the specific nonlinear equation.
Simplify both sides of the equation thoroughly.
Check if the left-hand side and the right-hand side of the equation are indeed equal.
Use a graphing calculator or a computer algebra system to verify the solution if possible.

Q: Can I use this method to verify solutions to differential equations?

A: No, this method is not suitable for verifying solutions to differential equations. Differential equations require different methods and techniques to solve and verify solutions.

Q: Are there any other methods to verify solutions to differential equations?

A: Yes, there are other methods to verify solutions to differential equations, including using numerical methods or approximation techniques.

Q: How do I choose the best method to verify a solution to a differential equation?

A: The best method to verify a solution to a differential equation depends on the specific equation and the tools available. You can choose the method that is most convenient and efficient for you.

Q: Can I use this method to solve differential equations?

A: No, this method is not suitable for solving differential equations. Differential equations require different methods and techniques to solve.

Q: Are there any tips or tricks to help me verify solutions to differential equations?

A: Yes, here are some tips and tricks to help you verify solutions to differential equations:

Make sure to use the correct method and technique for the specific differential equation.
Simplify both sides of the equation thoroughly.
Check if the left-hand side and the right-hand side of the equation are indeed equal.
Use a graphing calculator or a computer algebra system to verify the solution if possible.

Q: Can I use this method to verify solutions to systems of differential equations?

A: No, this method is not suitable for verifying solutions to systems of differential equations. Systems of differential equations require different methods and techniques to solve and verify solutions.

Q: Are there any other methods to verify solutions to systems of differential equations?

A: Yes, there are other methods to verify solutions to systems of differential equations, including using numerical methods or approximation techniques.

Q: How do I choose the best method to verify a solution to a system of differential equations?

A: The best method to verify a solution to a system of differential equations depends on the specific equations and the tools available. You can choose the method that is most convenient and efficient for you.

Q: Can I use this method to solve systems of differential equations?

A: No, this method is not suitable for solving systems of differential equations. Systems of differential equations require different methods and techniques to solve.

Q: Are there any tips or tricks to help me verify solutions to systems of differential equations?

A: Yes, here are some tips and tricks to help you verify solutions to systems of differential equations:

Make sure to use the correct method and technique for the specific system of differential equations.
Simplify both sides of the equation thoroughly.
Check if the left-hand side and the right-hand side of the equation are indeed equal.
Use a graphing calculator or a computer algebra system to verify the solution if possible.