Solving for the Value of m in a Linear Equation

Oct 13, 2025 by miodeya.com 16 views

Solving for the Value of m in a Linear Equation

Introduction

In algebra, solving for the value of a variable in a linear equation is a fundamental concept. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving for the value of m in the equation 1/2m - 3/4n = 16, given that n = 8.

Understanding the Equation

The given equation is 1/2m - 3/4n = 16. To solve for the value of m, we need to isolate m on one side of the equation. The equation involves two variables, m and n, and their coefficients are fractions. We will use algebraic techniques to simplify the equation and solve for m.

Substituting the Value of n

We are given that n = 8. We can substitute this value into the equation to get:

1/2m - 3/4(8) = 16

Simplifying the Equation

To simplify the equation, we need to evaluate the expression 3/4(8). This is equal to 6. So, the equation becomes:

1/2m - 6 = 16

Isolating m

To isolate m, we need to get rid of the constant term -6. We can do this by adding 6 to both sides of the equation:

1/2m = 16 + 6

Evaluating the Right-Hand Side

The right-hand side of the equation is 16 + 6, which is equal to 22. So, the equation becomes:

1/2m = 22

Solving for m

To solve for m, we need to get rid of the coefficient 1/2. We can do this by multiplying both sides of the equation by 2:

m = 22(2)

Evaluating the Right-Hand Side

The right-hand side of the equation is 22(2), which is equal to 44. So, the value of m is 44.

Conclusion

In this article, we solved for the value of m in the equation 1/2m - 3/4n = 16, given that n = 8. We used algebraic techniques to simplify the equation and isolate m. The value of m is 44.

Final Answer

The final answer is 44.

Discussion

This problem is a classic example of solving for the value of a variable in a linear equation. The key concept is to isolate the variable on one side of the equation and get rid of the constant term. The solution involves simplifying the equation, evaluating expressions, and using algebraic techniques to solve for the value of m.

References

[Algebra textbook]
[Online algebra resources]

Introduction

In the previous article, we solved for the value of m in the equation 1/2m - 3/4n = 16, given that n = 8. In this article, we will address some frequently asked questions (FAQs) about solving for the value of m.

Q: What is the first step in solving for the value of m?

A: The first step in solving for the value of m is to simplify the equation by getting rid of any fractions. This can be done by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: How do I simplify the equation 1/2m - 3/4n = 16?

A: To simplify the equation, we need to evaluate the expression 3/4(8). This is equal to 6. So, the equation becomes 1/2m - 6 = 16.

Q: How do I isolate m in the equation 1/2m - 6 = 16?

A: To isolate m, we need to get rid of the constant term -6. We can do this by adding 6 to both sides of the equation.

Q: What is the next step after isolating m?

A: After isolating m, we need to get rid of the coefficient 1/2. We can do this by multiplying both sides of the equation by 2.

Q: How do I evaluate the right-hand side of the equation m = 22(2)?

A: The right-hand side of the equation is 22(2), which is equal to 44.

Q: What is the value of m in the equation 1/2m - 3/4n = 16, given that n = 8?

A: The value of m is 44.

Q: What are some common mistakes to avoid when solving for the value of m?

A: Some common mistakes to avoid when solving for the value of m include:

Not simplifying the equation by getting rid of fractions
Not isolating m by getting rid of the constant term
Not getting rid of the coefficient 1/2
Not evaluating the right-hand side of the equation correctly

Q: How can I practice solving for the value of m?

A: You can practice solving for the value of m by working through examples and exercises in an algebra textbook or online resource. You can also try solving for the value of m in different equations to build your skills and confidence.

Q: What are some real-world applications of solving for the value of m?

A: Solving for the value of m has many real-world applications, including:

Physics: Solving for the value of m is used to calculate the mass of an object.
Engineering: Solving for the value of m is used to calculate the stress and strain on a material.
Economics: Solving for the value of m is used to calculate the cost of a product.

Conclusion

In this article, we addressed some frequently asked questions (FAQs) about solving for the value of m. We covered topics such as simplifying the equation, isolating m, and evaluating the right-hand side of the equation. We also discussed some common mistakes to avoid and provided some real-world applications of solving for the value of m.

Final Answer

The final answer is 44.

Discussion

This article is a continuation of the previous article, where we solved for the value of m in the equation 1/2m - 3/4n = 16, given that n = 8. In this article, we addressed some frequently asked questions (FAQs) about solving for the value of m.

References

[Algebra textbook]
[Online algebra resources]