Solve For \[$ N \$\]:$\[ \frac{5}{2} N = 98 - N \\]

Solving for n: A Step-by-Step Guide to Isolating the Variable

In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In this article, we will focus on solving for n in the given equation: $\frac{5}{2}n = 98 - n$. This equation is a linear equation, and solving for n will involve a series of algebraic manipulations.

Understanding the Equation

Before we dive into solving for n, let's take a closer look at the equation. The equation is a linear equation, which means it can be written in the form $ax + b = c$, where a, b, and c are constants. In this case, the equation is $\frac{5}{2}n = 98 - n$. Our goal is to isolate the variable n on one side of the equation.

Step 1: Multiply Both Sides by 2

To eliminate the fraction, we can multiply both sides of the equation by 2. This will give us: $5n = 2(98 - n)$. By multiplying both sides by 2, we are essentially getting rid of the fraction and making it easier to work with.

Step 2: Distribute the 2

Now that we have multiplied both sides by 2, we can distribute the 2 to the terms inside the parentheses. This will give us: $5n = 196 - 2n$. By distributing the 2, we are essentially multiplying each term inside the parentheses by 2.

Step 3: Add 2n to Both Sides

Our next step is to add 2n to both sides of the equation. This will give us: $5n + 2n = 196$. By adding 2n to both sides, we are essentially getting rid of the negative term and making it easier to work with.

Step 4: Combine Like Terms

Now that we have added 2n to both sides, we can combine like terms. In this case, the like terms are the 5n and 2n terms. By combining these terms, we get: $7n = 196$. By combining like terms, we are essentially simplifying the equation and making it easier to work with.

Step 5: Divide Both Sides by 7

Our final step is to divide both sides of the equation by 7. This will give us: $n = \frac{196}{7}$. By dividing both sides by 7, we are essentially isolating the variable n and solving for its value.

The Final Answer

After following these steps, we have successfully solved for n. The final answer is: $n = 28$. By following these steps, we have isolated the variable n and solved for its value.

Conclusion

Solving for n in the given equation involved a series of algebraic manipulations. By multiplying both sides by 2, distributing the 2, adding 2n to both sides, combining like terms, and dividing both sides by 7, we were able to isolate the variable n and solve for its value. This equation is a linear equation, and solving for n involved a series of algebraic manipulations. By following these steps, we have successfully solved for n and found its value.

Real-World Applications

Solving for n has many real-world applications. In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In physics, solving for n can be used to calculate the velocity of an object. In engineering, solving for n can be used to calculate the stress on a material. In economics, solving for n can be used to calculate the demand for a product.

Tips and Tricks

When solving for n, it's essential to follow the order of operations. This means that you should perform the operations in the following order: parentheses, exponents, multiplication and division, and addition and subtraction. By following the order of operations, you can ensure that you are solving for n correctly.

Common Mistakes

When solving for n, there are several common mistakes that you can make. One common mistake is to forget to multiply both sides by 2. Another common mistake is to forget to distribute the 2. By avoiding these common mistakes, you can ensure that you are solving for n correctly.

Conclusion

Solving for n in the given equation involved a series of algebraic manipulations. By multiplying both sides by 2, distributing the 2, adding 2n to both sides, combining like terms, and dividing both sides by 7, we were able to isolate the variable n and solve for its value. This equation is a linear equation, and solving for n involved a series of algebraic manipulations. By following these steps, we have successfully solved for n and found its value.
Solving for n: A Q&A Guide

In our previous article, we discussed how to solve for n in the equation $\frac{5}{2}n = 98 - n$. We walked through the steps of multiplying both sides by 2, distributing the 2, adding 2n to both sides, combining like terms, and dividing both sides by 7. In this article, we will answer some common questions that students may have when solving for n.

Q: What is the first step in solving for n?

A: The first step in solving for n is to multiply both sides of the equation by 2. This will eliminate the fraction and make it easier to work with.

Q: Why do I need to multiply both sides by 2?

A: You need to multiply both sides by 2 to eliminate the fraction. This will make it easier to work with the equation and isolate the variable n.

Q: What is the difference between multiplying and distributing?

A: Multiplying and distributing are two different operations. Multiplying involves multiplying each term in the equation by a constant, while distributing involves multiplying each term inside the parentheses by a constant.

Q: Why do I need to add 2n to both sides?

A: You need to add 2n to both sides to get rid of the negative term and make it easier to work with the equation.

Q: What is the purpose of combining like terms?

A: The purpose of combining like terms is to simplify the equation and make it easier to work with. By combining like terms, you can eliminate unnecessary terms and make the equation more manageable.

Q: Why do I need to divide both sides by 7?

A: You need to divide both sides by 7 to isolate the variable n and solve for its value.

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

A: Some common mistakes to avoid when solving for n include forgetting to multiply both sides by 2, forgetting to distribute the 2, and forgetting to add 2n to both sides. By avoiding these common mistakes, you can ensure that you are solving for n correctly.

Q: How do I know if I have solved for n correctly?

A: You can check if you have solved for n correctly by plugging the value of n back into the original equation. If the equation is true, then you have solved for n correctly.

Q: What are some real-world applications of solving for n?

A: Solving for n has many real-world applications. In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In physics, solving for n can be used to calculate the velocity of an object. In engineering, solving for n can be used to calculate the stress on a material. In economics, solving for n can be used to calculate the demand for a product.

Q: How can I practice solving for n?

A: You can practice solving for n by working through example problems and exercises. You can also try solving for n in different types of equations, such as linear equations and quadratic equations.

Q: What are some tips for solving for n?

A: Some tips for solving for n include following the order of operations, being careful with fractions and decimals, and checking your work to make sure you have solved for n correctly.

Conclusion

Solving for n is an essential skill in mathematics that involves isolating the variable n on one side of the equation. By following the steps outlined in this article, you can solve for n in a variety of equations. Remember to multiply both sides by 2, distribute the 2, add 2n to both sides, combine like terms, and divide both sides by 7. With practice and patience, you can become proficient in solving for n and apply this skill to a variety of real-world problems.