Solve For { N $} : : : { -18 = \frac{n}{4} - 25 \}

by ADMIN 51 views

Introduction

In mathematics, solving for a variable in an equation is a fundamental concept that is used to find the value of the variable. In this article, we will focus on solving for the variable n in the equation -18 = (n/4) - 25. This equation involves fractions and linear equations, and we will use algebraic techniques to solve for n.

Understanding the Equation

The given equation is -18 = (n/4) - 25. To solve for n, we need to isolate the variable n on one side of the equation. The equation involves a fraction, which can be simplified by multiplying both sides of the equation by the denominator of the fraction.

Step 1: Multiply Both Sides by 4

To eliminate the fraction, we can multiply both sides of the equation by 4. This will give us:

-18 × 4 = (n/4) × 4 - 25 × 4

Simplifying the Equation

Multiplying both sides of the equation by 4 gives us:

-72 = n - 100

Step 2: Add 100 to Both Sides

To isolate the variable n, we can add 100 to both sides of the equation. This will give us:

-72 + 100 = n - 100 + 100

Simplifying the Equation

Adding 100 to both sides of the equation gives us:

28 = n

Conclusion

In this article, we solved for the variable n in the equation -18 = (n/4) - 25. We used algebraic techniques to isolate the variable n on one side of the equation. By multiplying both sides of the equation by 4 and adding 100 to both sides, we were able to find the value of n, which is 28.

Tips and Tricks

  • When solving for a variable in an equation, it is essential to isolate the variable on one side of the equation.
  • To eliminate fractions, multiply both sides of the equation by the denominator of the fraction.
  • When adding or subtracting numbers, make sure to add or subtract the same numbers from both sides of the equation.

Real-World Applications

Solving for a variable in an equation has numerous real-world applications. For example, in physics, solving for a variable can help us understand the motion of objects. In finance, solving for a variable can help us understand the value of investments. In engineering, solving for a variable can help us design and build structures.

Common Mistakes

When solving for a variable in an equation, there are several common mistakes that can be made. These include:

  • Not isolating the variable on one side of the equation
  • Not eliminating fractions
  • Not adding or subtracting the same numbers from both sides of the equation

Final Thoughts

Solving for a variable in an equation is a fundamental concept in mathematics that has numerous real-world applications. By following the steps outlined in this article, we can solve for a variable in an equation and understand the value of the variable. Remember to isolate the variable on one side of the equation, eliminate fractions, and add or subtract the same numbers from both sides of the equation.

Additional Resources

For more information on solving for a variable in an equation, check out the following resources:

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

Conclusion

In conclusion, solving for a variable in an equation is a fundamental concept in mathematics that has numerous real-world applications. By following the steps outlined in this article, we can solve for a variable in an equation and understand the value of the variable. Remember to isolate the variable on one side of the equation, eliminate fractions, and add or subtract the same numbers from both sides of the equation.

Introduction

In our previous article, we solved for the variable n in the equation -18 = (n/4) - 25. In this article, we will answer some frequently asked questions about solving for n in this equation.

Q: What is the first step in solving for n in the equation -18 = (n/4) - 25?

A: The first step in solving for n in the equation -18 = (n/4) - 25 is to multiply both sides of the equation by 4. This will eliminate the fraction and make it easier to solve for n.

Q: Why do we need to multiply both sides of the equation by 4?

A: We need to multiply both sides of the equation by 4 because the fraction (n/4) is multiplied by 4, which will eliminate the fraction and make it easier to solve for n.

Q: What is the next step in solving for n in the equation -18 = (n/4) - 25?

A: The next step in solving for n in the equation -18 = (n/4) - 25 is to add 100 to both sides of the equation. This will isolate the variable n on one side of the equation.

Q: Why do we need to add 100 to both sides of the equation?

A: We need to add 100 to both sides of the equation because the equation is -18 = (n/4) - 25, and we need to get rid of the -25 on the right-hand side of the equation. By adding 100 to both sides of the equation, we can eliminate the -25 and isolate the variable n.

Q: What is the final answer to the equation -18 = (n/4) - 25?

A: The final answer to the equation -18 = (n/4) - 25 is n = 28.

Q: Can you explain the concept of isolating the variable n on one side of the equation?

A: Yes, isolating the variable n on one side of the equation means that we need to get the variable n by itself on one side of the equation, without any other numbers or variables on the same side. In the equation -18 = (n/4) - 25, we need to isolate the variable n by getting rid of the -25 on the right-hand side of the equation.

Q: What are some common mistakes that people make when solving for n in the equation -18 = (n/4) - 25?

A: Some common mistakes that people make when solving for n in the equation -18 = (n/4) - 25 include:

  • Not multiplying both sides of the equation by 4
  • Not adding 100 to both sides of the equation
  • Not isolating the variable n on one side of the equation

Q: How can I practice solving for n in the equation -18 = (n/4) - 25?

A: You can practice solving for n in the equation -18 = (n/4) - 25 by trying different values of n and seeing if you can get the correct answer. You can also try solving for n in other equations that involve fractions and linear equations.

Q: What are some real-world applications of solving for n in the equation -18 = (n/4) - 25?

A: Some real-world applications of solving for n in the equation -18 = (n/4) - 25 include:

  • Physics: Solving for n in the equation -18 = (n/4) - 25 can help us understand the motion of objects.
  • Finance: Solving for n in the equation -18 = (n/4) - 25 can help us understand the value of investments.
  • Engineering: Solving for n in the equation -18 = (n/4) - 25 can help us design and build structures.

Conclusion

In this article, we answered some frequently asked questions about solving for n in the equation -18 = (n/4) - 25. We covered topics such as multiplying both sides of the equation by 4, adding 100 to both sides of the equation, and isolating the variable n on one side of the equation. We also discussed some common mistakes that people make when solving for n in this equation and provided some real-world applications of solving for n in this equation.