Solve For \[$ N \$\].$\[ -75 = N + 9 \\]

Feb 27, 2025 by ADMIN 41 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 simple linear equation of the form -75 = n + 9. We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at what it means. The equation -75 = n + 9 is a linear equation, which means that it is an equation in which the highest power of the variable (in this case, n) is 1. The equation is also a simple linear equation, which means that it can be solved using basic algebraic operations.

Step 1: Isolate the Variable

The first step in solving the equation is to isolate the variable n. To do this, we need to get rid of the constant term on the right-hand side of the equation. In this case, the constant term is 9. We can do this by subtracting 9 from both sides of the equation.

-75 = n + 9
-75 - 9 = n + 9 - 9
-84 = n

Step 2: Solve for n

Now that we have isolated the variable n, we can solve for its value. To do this, we need to get rid of the negative sign in front of the 84. We can do this by multiplying both sides of the equation by -1.

-84 = n
-1 \* -84 = -1 \* n
84 = n

Conclusion

In this article, we have solved a simple linear equation of the form -75 = n + 9. We broke down the solution into two steps: isolating the variable and solving for its value. By following these steps, we were able to find the value of n, which is 84.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations like this one:

Make sure to isolate the variable before solving for its value.
Use basic algebraic operations, such as addition, subtraction, multiplication, and division, to solve the equation.
Check your work by plugging the solution back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

Not isolating the variable before solving for its value.
Not using basic algebraic operations to solve the equation.
Not checking your work by plugging the solution back into the original equation.

Real-World Applications

Linear equations have many real-world applications, including:

Physics: Linear equations are used to describe the motion of objects under constant acceleration.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve simple linear equations like -75 = n + 9. Remember to isolate the variable before solving for its value, and use basic algebraic operations to solve the equation. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.

Additional Resources

If you want to learn more about solving linear equations, here are some additional resources:

Khan Academy: Linear Equations
Mathway: Linear Equations
Wolfram Alpha: Linear Equations

Final Thoughts

Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that practice makes perfect, and sometimes, it's helpful to have a refresher on the concepts. In this article, we will answer some frequently asked questions about solving linear equations, providing you with a deeper understanding of the subject.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation that can be written in the form ax + b = c, where a, b, and c 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 can be done by using basic algebraic operations, such as addition, subtraction, multiplication, and division. You can also use inverse operations to get rid of the constant term on the right-hand side of the equation.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. In other words, a linear equation can be written in the form ax + b = c, while a quadratic equation can be written in the form ax^2 + bx + c = 0.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable. If the highest power is 1, then the equation is linear. If the highest power is 2, then the equation is quadratic.

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

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

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

Not isolating the variable before solving for its value.
Not using basic algebraic operations to solve the equation.
Not checking your work by plugging the solution back into the original equation.

Q: How do I apply linear equations to real-world problems?

A: Linear equations have many real-world applications, including:

Physics: Linear equations are used to describe the motion of objects under constant acceleration.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model economic systems and make predictions about future trends.

Q: What are some additional resources for learning about linear equations?

A: Some additional resources for learning about linear equations include:

Khan Academy: Linear Equations
Mathway: Linear Equations
Wolfram Alpha: Linear Equations

Conclusion

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it has many real-world applications. By mastering this skill, you will be able to solve a wide range of problems and make predictions about future trends. Remember to practice regularly and seek help when you need it. With dedication and hard work, you will become proficient in solving linear equations and be able to apply them to real-world problems.