Solve For \[$ N \$\].$\[ 15.95 = 3.19n \\]

Feb 26, 2025 by ADMIN 43 views

Introduction

In mathematics, solving for a variable is a fundamental concept that is used to find the value of a variable in an equation. In this article, we will focus on solving for the variable n in the equation 15.95 = 3.19n. This equation is a simple linear equation, and we will use algebraic methods to solve for n.

Understanding the Equation

The given equation is 15.95 = 3.19n. To solve for n, we need to isolate the variable n on one side of the equation. The equation is already in the form of a linear equation, where the variable n is multiplied by a constant (3.19). Our goal is to find the value of n that satisfies the equation.

Solving for n

To solve for n, we can use the following steps:

Divide both sides of the equation by 3.19. This will isolate the variable n on the left-hand side of the equation.

Step-by-Step Solution

Step 1: Divide Both Sides by 3.19

To solve for n, we need to divide both sides of the equation by 3.19. This will give us the value of n.

15.95 ÷ 3.19 = n

Step 2: Calculate the Value of n

Now, we need to calculate the value of n by dividing 15.95 by 3.19.

n = 15.95 ÷ 3.19
n = 4.99

Conclusion

In this article, we solved for the variable n in the equation 15.95 = 3.19n. We used algebraic methods to isolate the variable n on one side of the equation and found the value of n to be 4.99. This is a simple example of solving for a variable in a linear equation.

Real-World Applications

Solving for a variable is a fundamental concept in mathematics that has many real-world applications. In finance, for example, solving for a variable can be used to calculate the value of an investment or the return on investment. In science, solving for a variable can be used to calculate the value of a physical quantity, such as the speed of an object or the force exerted on an object.

Tips and Tricks

Here are some tips and tricks to help you solve for a variable:

Always read the equation carefully and understand what is being asked.
Use algebraic methods to isolate the variable on one side of the equation.
Check your work by plugging the value of the variable back into the original equation.
Use a calculator to check your work and ensure that you have the correct value.

Common Mistakes

Here are some common mistakes to avoid when solving for a variable:

Not reading the equation carefully and understanding what is being asked.
Not using algebraic methods to isolate the variable on one side of the equation.
Not checking your work by plugging the value of the variable back into the original equation.
Not using a calculator to check your work and ensure that you have the correct value.

Final Thoughts

Solving for a variable is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article and using algebraic methods to isolate the variable on one side of the equation, you can solve for a variable and find the value of the variable. Remember to always read the equation carefully, use algebraic methods, and check your work to ensure that you have the correct value.

Introduction

In our previous article, we solved for the variable n in the equation 15.95 = 3.19n. In this article, we will answer some frequently asked questions (FAQs) related to solving for a variable in a linear equation.

Q&A

Q: What is the first step in solving for a variable in a linear equation?

A: The first step in solving for a variable in a linear equation is to read the equation carefully and understand what is being asked. Then, use algebraic methods to isolate the variable on one side of the equation.

Q: How do I isolate the variable on one side of the equation?

A: To isolate the variable on one side of the equation, you can use the following steps:

Add or subtract the same value to both sides of the equation to get rid of any constants on the same side as the variable.
Multiply or divide both sides of the equation by the same value to get rid of any coefficients on the same side as the variable.

Q: What is the difference between a coefficient and a constant?

A: A coefficient is a number that is multiplied by a variable, while a constant is a number that is not multiplied by a variable. For example, in the equation 2x + 3 = 5, the coefficient of x is 2, and the constant is 3.

Q: How do I check my work when solving for a variable?

A: To check your work when solving for a variable, you can plug the value of the variable back into the original equation and see if it is true. If it is true, then you have solved for the variable correctly.

Q: What are some common mistakes to avoid when solving for a variable?

A: Some common mistakes to avoid when solving for a variable include:

Not reading the equation carefully and understanding what is being asked.
Not using algebraic methods to isolate the variable on one side of the equation.
Not checking your work by plugging the value of the variable back into the original equation.
Not using a calculator to check your work and ensure that you have the correct value.

Q: Can I use a calculator to solve for a variable?

A: Yes, you can use a calculator to solve for a variable. However, it is always a good idea to check your work by plugging the value of the variable back into the original equation to ensure that you have the correct value.

Q: What are some real-world applications of solving for a variable?

A: Solving for a variable has many real-world applications, including:

Finance: Solving for a variable can be used to calculate the value of an investment or the return on investment.
Science: Solving for a variable can be used to calculate the value of a physical quantity, such as the speed of an object or the force exerted on an object.
Engineering: Solving for a variable can be used to design and optimize systems, such as bridges or buildings.

Conclusion

Final Thoughts

Solving for a variable is a skill that is used in many areas of mathematics and science. By practicing and mastering this skill, you can become a more confident and proficient problem-solver. Remember to always check your work and use a calculator to ensure that you have the correct value.