Solve For { N $} : : : { -n + 5 = N - 11 \}

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, where the variable n is isolated on one side of the equation. We will use the given equation -n + 5 = n - 11 as an example to demonstrate the step-by-step process of solving for n.

Understanding the Equation

The given equation is -n + 5 = n - 11. This equation is a linear equation, which means 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, as it can be solved using basic algebraic operations.

Step 1: Add n to Both Sides of the Equation

To solve for n, we need to isolate the variable on one side of the equation. The first step is to add n to both sides of the equation. This will eliminate the negative sign in front of the n term.

-n + 5 = n - 11
-n + n + 5 = n - n - 11
0 + 5 = -11

Step 2: Simplify the Equation

After adding n to both sides of the equation, we are left with 0 + 5 = -11. We can simplify this equation by combining the constants on the left-hand side.

0 + 5 = -11
5 = -11

Step 3: Add 11 to Both Sides of the Equation

Now that we have simplified the equation, we need to get rid of the negative sign in front of the -11 term. We can do this by adding 11 to both sides of the equation.

5 = -11
5 + 11 = -11 + 11
16 = 0

Step 4: Simplify the Equation

After adding 11 to both sides of the equation, we are left with 16 = 0. We can simplify this equation by combining the constants on the left-hand side.

16 = 0

Conclusion

Unfortunately, the equation 16 = 0 is a contradiction, which means that there is no solution for n. This is because the left-hand side of the equation (16) is a positive number, while the right-hand side of the equation (0) is a zero. These two values cannot be equal, and therefore, there is no value of n that can satisfy the equation.

Final Answer

The final answer is $\boxed{No solution}$.

Why is this Equation Unsolvable?

The equation -n + 5 = n - 11 is unsolvable because it is a contradiction. When we add n to both sides of the equation, we get 0 + 5 = -11, which simplifies to 5 = -11. This is a contradiction because 5 and -11 are not equal. Therefore, there is no value of n that can satisfy the equation.

What is the Importance of Solving Linear Equations?

Solving linear equations is an important skill in mathematics because it helps us to understand the relationships between variables. In real-world applications, linear equations are used to model a wide range of phenomena, from the motion of objects to the growth of populations. By solving linear equations, we can gain insights into the behavior of these phenomena and make predictions about future outcomes.

How to Solve Linear Equations?

To solve linear equations, we need to follow a series of steps. First, we need to add or subtract the same value to both sides of the equation to eliminate any negative signs or fractions. Next, we need to multiply or divide both sides of the equation by the same value to eliminate any fractions. Finally, we need to isolate the variable on one side of the equation by adding or subtracting the same value to both sides.

Common Mistakes to Avoid When Solving Linear Equations

When solving linear equations, there are several common mistakes to avoid. First, we need to make sure that we are following the correct order of operations. This means that we need to perform any calculations inside parentheses first, followed by any exponents, and finally any multiplication and division. Second, we need to make sure that we are isolating the variable on one side of the equation. This means that we need to add or subtract the same value to both sides of the equation to eliminate any negative signs or fractions. Finally, we need to make sure that we are checking our work to ensure that the equation is true.

Conclusion

Solving linear equations is an important skill in mathematics that helps us to understand the relationships between variables. By following a series of steps and avoiding common mistakes, we can solve linear equations and gain insights into the behavior of real-world phenomena. In this article, we used the equation -n + 5 = n - 11 as an example to demonstrate the step-by-step process of solving for n. We also discussed the importance of solving linear equations and provided tips for avoiding common mistakes.

Introduction

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the steps involved in solving these equations. In this article, we will provide a Q&A guide to help you understand the process of solving linear equations.

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. It's a simple equation that can be solved using basic algebraic operations.

Q: What are the steps involved in solving a linear equation?

A: The steps involved in solving a linear equation are:

1. Add or subtract the same value to both sides of the equation to eliminate any negative signs or fractions.
2. Multiply or divide both sides of the equation by the same value to eliminate any fractions.
3. Isolate the variable on one side of the equation by adding or subtracting the same value to both sides.

Q: How do I add or subtract the same value to both sides of the equation?

A: To add or subtract the same value to both sides of the equation, you need to follow these steps:

1. Identify the value that needs to be added or subtracted from both sides.
2. Add or subtract that value from both sides of the equation.
3. Simplify the equation by combining like terms.

Q: How do I multiply or divide both sides of the equation by the same value?

A: To multiply or divide both sides of the equation by the same value, you need to follow these steps:

1. Identify the value that needs to be multiplied or divided from both sides.
2. Multiply or divide both sides of the equation by that value.
3. Simplify the equation by combining like terms.

Q: What is the importance of isolating the variable on one side of the equation?

A: Isolating the variable on one side of the equation is crucial because it allows you to find the value of the variable. When the variable is isolated on one side of the equation, you can easily determine its value by solving for it.

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

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

1. Not following the correct order of operations.
2. Not isolating the variable on one side of the equation.
3. Not checking your work to ensure that the equation is true.

Q: How do I check my work to ensure that the equation is true?

A: To check your work, you need to follow these steps:

1. Plug in the value of the variable into the original equation.
2. Simplify the equation by combining like terms.
3. Check if the equation is true.

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

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

1. Modeling the motion of objects.
2. Calculating the growth of populations.
3. Determining the cost of goods and services.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to follow these steps:

1. Multiply or divide both sides of the equation by the least common multiple (LCM) of the denominators.
2. Simplify the equation by combining like terms.
3. Isolate the variable on one side of the equation.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, you need to follow these steps:

1. Multiply or divide both sides of the equation by 10 to eliminate the decimals.
2. Simplify the equation by combining like terms.
3. Isolate the variable on one side of the equation.

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the steps involved in solving these equations. By following the steps outlined in this Q&A guide, you can solve linear equations and gain insights into the behavior of real-world phenomena. Remember to avoid common mistakes and check your work to ensure that the equation is true.