Solve For N N N : 5 6 N = 10 \frac{5}{6} N = 10 6 5 N = 10 A. 2 B. 10 C. 12 D. 60

Mar 9, 2025 by ADMIN 87 views

**Solving Linear Equations: A Step-by-Step Guide**

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear equation, namely the equation $\frac{5}{6} n = 10$ . We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $n$ ) is 1. Linear equations can be written in the form $ax = b$ , where $a$ and $b$ are constants, and $x$ is the variable. In our example, the equation $\frac{5}{6} n = 10$ is a linear equation because the highest power of $n$ is 1.

The Solution Process

To solve the equation $\frac{5}{6} n = 10$ , we need to isolate the variable $n$ . This means that we need to get rid of the fraction and the constant on the same side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction, which is $\frac{6}{5}$ .

Step 1: Multiply Both Sides by the Reciprocal

To get rid of the fraction, we need to multiply both sides of the equation by the reciprocal of the fraction, which is $\frac{6}{5}$ . This will cancel out the fraction and leave us with a simple equation.

\frac{5}{6} n = 10
\Rightarrow \frac{6}{5} \cdot \frac{5}{6} n = \frac{6}{5} \cdot 10
\Rightarrow n = \frac{6}{5} \cdot 10

Step 2: Simplify the Right-Hand Side

Now that we have multiplied both sides of the equation by the reciprocal, we can simplify the right-hand side. We can do this by multiplying the numbers together.

n = \frac{6}{5} \cdot 10
\Rightarrow n = \frac{60}{5}
\Rightarrow n = 12

Conclusion

In this article, we have solved the linear equation $\frac{5}{6} n = 10$ using a step-by-step approach. We have shown that the solution is $n = 12$ . This is a simple example of how to solve a linear equation, and it illustrates the importance of following the correct steps to isolate the variable.

Why is Solving Linear Equations Important?

Solving linear equations is an essential skill for students to master because it is used in a wide range of applications, including science, engineering, economics, and finance. Linear equations are used to model real-world situations, such as the motion of objects, the growth of populations, and the behavior of financial markets. By solving linear equations, students can develop a deeper understanding of these applications and make informed decisions.

Real-World Applications of Linear Equations

Linear equations have many real-world applications, including:

Physics: Linear equations are used to model the motion of objects, including the trajectory of projectiles and the motion of objects under the influence of gravity.
Economics: Linear equations are used to model the behavior of economic systems, including the supply and demand of goods and services.
Finance: Linear equations are used to model the behavior of financial markets, including the movement of stock prices and the behavior of interest rates.
Biology: Linear equations are used to model the growth of populations, including the growth of bacteria and the spread of diseases.

Conclusion

In conclusion, solving linear equations is an essential skill for students to master. By following the correct steps, students can solve linear equations and develop a deeper understanding of the applications of linear equations in real-world situations. Whether it is modeling the motion of objects, the growth of populations, or the behavior of financial markets, linear equations are an essential tool for making informed decisions.

Final Answer

The final answer to the equation $\frac{5}{6} n = 10$ is:

A. 2: Incorrect
B. 10: Incorrect
C. 12: Correct
D. 60: Incorrect
Solving Linear Equations: A Q&A Guide =====================================

Introduction

In our previous article, we discussed how to solve linear equations using a step-by-step approach. In this article, we will provide a Q&A guide to help students understand the concept of linear equations and how to solve them.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $n$ ) is 1. Linear equations can be written in the form $ax = b$ , where $a$ and $b$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable. This means that you need to get rid of the fraction and the constant on the same side of the equation. You can do this by multiplying both sides of the equation by the reciprocal of the fraction.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$ .

Q: How do I multiply both sides of the equation by the reciprocal?

A: To multiply both sides of the equation by the reciprocal, you need to multiply the fraction on the left-hand side by the reciprocal, and then multiply the constant on the right-hand side by the reciprocal.

Q: What if the equation has a coefficient?

A: If the equation has a coefficient, you need to multiply both sides of the equation by the reciprocal of the coefficient. For example, if the equation is $2x = 10$ , you need to multiply both sides of the equation by $\frac{1}{2}$ .

Q: What if the equation has a negative sign?

A: If the equation has a negative sign, you need to multiply both sides of the equation by the reciprocal of the fraction, and then change the sign of the constant on the right-hand side.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it is always a good idea to check your answer by plugging it back into the original equation.

Q: What if I get a negative answer?

A: If you get a negative answer, it means that the equation has no solution. This can happen if the equation is inconsistent, or if the variable is not defined.

Q: Can I use linear equations to solve real-world problems?

A: Yes, you can use linear equations to solve real-world problems. Linear equations are used to model a wide range of applications, including science, engineering, economics, and finance.

Q: What are some examples of real-world applications of linear equations?

A: Some examples of real-world applications of linear equations include:

Physics: Linear equations are used to model the motion of objects, including the trajectory of projectiles and the motion of objects under the influence of gravity.
Economics: Linear equations are used to model the behavior of economic systems, including the supply and demand of goods and services.
Finance: Linear equations are used to model the behavior of financial markets, including the movement of stock prices and the behavior of interest rates.
Biology: Linear equations are used to model the growth of populations, including the growth of bacteria and the spread of diseases.

Conclusion

Final Tips

Practice, practice, practice: The more you practice solving linear equations, the more comfortable you will become with the process.
Use a calculator: If you are unsure about the solution, use a calculator to check your answer.
Check your work: Always check your work by plugging the solution back into the original equation.
Use linear equations to solve real-world problems: Linear equations are used to model a wide range of applications, including science, engineering, economics, and finance.