Solve For \[$ N \$\].$\[ -17 + \frac{n}{-3} = -12 \\]

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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, which involves isolating the variable (in this case, n) on one side of the equation. We will use a step-by-step approach to solve the equation -17 + n/-3 = -12.

Understanding the Equation

Before we dive into solving the equation, let's break it down and understand what it means. The equation is -17 + n/-3 = -12. This equation states that the sum of -17 and n divided by -3 is equal to -12. Our goal is to isolate the variable n and find its value.

Step 1: Simplify the Equation

To simplify the equation, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by -3. This will eliminate the fraction and make it easier to work with.

-17 + n/-3 = -12
-3(-17 + n/-3) = -3(-12)

Step 2: Distribute the Negative 3

Now that we have multiplied both sides of the equation by -3, we need to distribute the negative 3 to the terms inside the parentheses.

-3(-17 + n/-3) = -3(-12)
33 - n = 36

Step 3: Isolate the Variable

Our goal is to isolate the variable n, so we need to get rid of the constant term on the same side as n. We can do this by subtracting 33 from both sides of the equation.

33 - n = 36
-n = 36 - 33
-n = 3

Step 4: Solve for n

Now that we have isolated the variable n, we can solve for its value. To do this, we need to multiply both sides of the equation by -1.

-n = 3
n = -3

Conclusion

In this article, we have solved a linear equation using a step-by-step approach. We started by simplifying the equation, distributing the negative 3, isolating the variable, and finally solving for n. The value of n is -3.

Tips and Tricks

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

  • Always start by simplifying the equation.
  • Use the distributive property to eliminate fractions.
  • Isolate the variable by getting rid of the constant term on the same side as the variable.
  • Use inverse operations to solve for the variable.

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.

Common Mistakes

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

  • Not simplifying the equation before solving.
  • Not using the distributive property to eliminate fractions.
  • Not isolating the variable by getting rid of the constant term on the same side as the variable.
  • Not using inverse operations to solve for the variable.

Practice Problems

Here are some practice problems to help you reinforce your understanding of solving linear equations:

  • Solve the equation 2x + 5 = 11.
  • Solve the equation x - 3 = 7.
  • Solve the equation 4x - 2 = 10.

Conclusion

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 you reinforce your understanding 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, x or n) is 1. Linear equations can be written in the form ax + b = c, where a, b, and c are constants.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to get rid of any fractions or decimals. You can do this by multiplying both sides of the equation by the denominator of the fraction or by multiplying both sides by 10 to eliminate the decimal.

Q: What is the distributive property?

A: The distributive property is a rule that allows you to multiply a single term to multiple terms inside parentheses. For example, 2(x + 3) = 2x + 6.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, you need to get rid of the constant term on the same side as the variable. You can do this by adding or subtracting the same value to both sides of the equation.

Q: What is the inverse operation?

A: The inverse operation is a mathematical operation that undoes the effect of another operation. For example, the inverse of addition is subtraction, and the inverse of multiplication is division.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to apply the inverse operation to both sides of the equation. For example, if you have the equation 2x + 5 = 11, you can subtract 5 from both sides to get 2x = 6, and then divide both sides by 2 to get x = 3.

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

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

  • Not simplifying the equation before solving.
  • Not using the distributive property to eliminate fractions.
  • Not isolating the variable by getting rid of the constant term on the same side as the variable.
  • Not using inverse operations to solve for the variable.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through practice problems, such as the ones listed below:

  • Solve the equation 2x + 5 = 11.
  • Solve the equation x - 3 = 7.
  • Solve the equation 4x - 2 = 10.

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

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.

Conclusion

Solving linear equations is a crucial skill for students to master. By following a step-by-step approach and using inverse operations, we can solve linear equations and find the value of the variable. Remember to simplify the equation, distribute the negative 3, isolate the variable, and finally solve for n. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.

Practice Problems

Here are some practice problems to help you reinforce your understanding of solving linear equations:

  • Solve the equation 2x + 5 = 11.
  • Solve the equation x - 3 = 7.
  • Solve the equation 4x - 2 = 10.

Additional Resources

Here are some additional resources to help you learn more about solving linear equations:

  • Khan Academy: Solving Linear Equations
  • Mathway: Solving Linear Equations
  • IXL: Solving Linear Equations