Solve $14n + 6p - 8n = 18p$ For $n$.A. $n = \frac{R}{2}$ B. $n = 2p$ C. $n = 4p$ D. $n = \frac{?}{4}$

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 linear equation, $14n + 6p - 8n = 18p$, for the variable $n$. We will break down the solution step by step, using algebraic manipulations to isolate the variable $n$.

Understanding the Equation

Before we dive into the solution, let's take a closer look at the equation:

$$14n + 6p - 8n = 18p$$

This equation is a linear equation in two variables, $n$ and $p$. The goal is to solve for $n$ in terms of $p$.

Step 1: Combine Like Terms

The first step in solving the equation is to combine like terms. In this case, we have two terms with the variable $n$: $14n$ and $-8n$. We can combine these terms by adding their coefficients:

$$14n - 8n = 6n$$

So, the equation becomes:

$$6n + 6p = 18p$$

Step 2: Isolate the Variable $n$

Now that we have combined like terms, we can isolate the variable $n$ by subtracting $6p$ from both sides of the equation:

$$6n = 18p - 6p$$

Simplifying the right-hand side, we get:

$$6n = 12p$$

Step 3: Solve for $n$

Finally, we can solve for $n$ by dividing both sides of the equation by $6$:

$$n = \frac{12p}{6}$$

Simplifying the fraction, we get:

$$n = 2p$$

Conclusion

In this article, we solved the linear equation $14n + 6p - 8n = 18p$ for the variable $n$. By combining like terms, isolating the variable $n$, and solving for $n$, we arrived at the solution:

$$n = 2p$$

This solution shows that the variable $n$ is directly proportional to the variable $p$. The constant of proportionality is $2$.

Answer Key

Based on the solution, the correct answer is:

B. $n = 2p$

Additional Tips and Resources

If you are struggling to solve linear equations, here are some additional tips and resources to help you:

• Practice, practice, practice! The more you practice solving linear equations, the more comfortable you will become with the process.
• Use online resources, such as Khan Academy or Mathway, to get additional practice and support.
• Watch video tutorials or online lectures to help you understand the concepts and techniques.
• Join a study group or find a study buddy to work through problems together.

Introduction

In our previous article, we solved the linear equation $14n + 6p - 8n = 18p$ for the variable $n$. We received many questions from readers who were struggling to understand the solution. In this article, we will address some of the most common questions and provide additional guidance on solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form:

$$ax + by = c$$

where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables.

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

A: To determine if an equation is linear, look for the following characteristics:

• The highest power of the variable(s) is 1.
• The equation can be written in the form $ax + by = c$.
• The equation does not contain any exponents or roots.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example:

• Linear equation: $2x + 3y = 5$
• Quadratic equation: $x^2 + 4x + 4 = 0$

Q: How do I solve a linear equation?

A: To solve a linear equation, follow these steps:

1. Combine like terms.
2. Isolate the variable(s) by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
3. Solve for the variable(s) by performing the necessary operations.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I use the order of operations to solve an equation?

A: To use the order of operations to solve an equation, follow these steps:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division operations from left to right.
4. Evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation with one or more variables, while a system of linear equations is a set of two or more linear equations with the same variables. For example:

• Linear equation: $2x + 3y = 5$
• System of linear equations: $2x + 3y = 5$ and $x - 2y = -3$

Conclusion

In this article, we addressed some of the most common questions about solving linear equations. We provided additional guidance on the order of operations and the difference between linear equations and systems of linear equations. By following these tips and resources, you will be well on your way to mastering the art of solving linear equations.

Additional Tips and Resources

If you are struggling to solve linear equations, here are some additional tips and resources to help you:

• Practice, practice, practice! The more you practice solving linear equations, the more comfortable you will become with the process.
• Use online resources, such as Khan Academy or Mathway, to get additional practice and support.
• Watch video tutorials or online lectures to help you understand the concepts and techniques.
• Join a study group or find a study buddy to work through problems together.

By following these tips and resources, you will be well on your way to mastering the art of solving linear equations.