Simplify Your Answer.$-18 = -\frac{3}{2} N$

Simplify Your Answer: Understanding the Equation $-18 = -\frac{3}{2} n$

In mathematics, equations are a fundamental concept that help us solve problems and understand relationships between variables. One of the most common types of equations is the linear equation, which can be written in the form of $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable. In this article, we will focus on simplifying the equation $-18 = -\frac{3}{2} n$, which is a linear equation with a variable $n$. We will break down the steps to simplify this equation and provide a clear understanding of the concept.

The equation $-18 = -\frac{3}{2} n$ is a linear equation with a variable $n$. The left-hand side of the equation is a constant, $-18$, while the right-hand side is an expression involving the variable $n$. To simplify this equation, we need to isolate the variable $n$ and express it in terms of a single value.

Step 1: Multiply Both Sides by 2

To simplify the equation, we can start by multiplying both sides of the equation by 2. This will eliminate the fraction on the right-hand side and make it easier to work with.

-18 = -\frac{3}{2} n
\implies -18 \times 2 = -\frac{3}{2} n \times 2
\implies -36 = -3n

Step 2: Divide Both Sides by -3

Now that we have eliminated the fraction, we can divide both sides of the equation by -3 to isolate the variable $n$.

-36 = -3n
\implies \frac{-36}{-3} = \frac{-3n}{-3}
\implies 12 = n

In conclusion, the equation $-18 = -\frac{3}{2} n$ can be simplified by multiplying both sides by 2 and then dividing both sides by -3. This results in the value of $n$ being equal to 12. By following these steps, we have successfully simplified the equation and isolated the variable $n$.

• When working with fractions, it's often helpful to multiply both sides of the equation by a common denominator to eliminate the fraction.
• When dividing both sides of the equation by a constant, make sure to check if the constant is positive or negative, as this can affect the sign of the result.
• Always check your work by plugging the solution back into the original equation to ensure that it is true.

Simplifying equations like $-18 = -\frac{3}{2} n$ has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, equations like this can be used to describe the motion of objects and predict their behavior. In engineering, equations like this can be used to design and optimize systems. In economics, equations like this can be used to model and analyze economic systems.

• One common mistake when simplifying equations is to forget to multiply or divide both sides of the equation by the same value.
• Another common mistake is to forget to check the sign of the constant when dividing both sides of the equation.
• A third common mistake is to not check the work by plugging the solution back into the original equation.

In conclusion, simplifying equations like $-18 = -\frac{3}{2} n$ is an important skill that has many real-world applications. By following the steps outlined in this article, you can successfully simplify equations and isolate variables. Remember to always check your work and be mindful of common mistakes. With practice and patience, you will become proficient in simplifying equations and solving problems.
Simplify Your Answer: Understanding the Equation $-18 = -\frac{3}{2} n$ - Q&A

In our previous article, we discussed how to simplify the equation $-18 = -\frac{3}{2} n$. We broke down the steps to isolate the variable $n$ and provided a clear understanding of the concept. In this article, we will answer some frequently asked questions related to simplifying equations like $-18 = -\frac{3}{2} n$.

Q: What is the first step to simplify the equation $-18 = -\frac{3}{2} n$?

A: The first step to simplify the equation $-18 = -\frac{3}{2} n$ is to multiply both sides of the equation by 2. This will eliminate the fraction on the right-hand side and make it easier to work with.

Q: Why do we multiply both sides of the equation by 2?

A: We multiply both sides of the equation by 2 to eliminate the fraction on the right-hand side. This makes it easier to work with and allows us to isolate the variable $n$.

Q: What is the next step after multiplying both sides of the equation by 2?

A: After multiplying both sides of the equation by 2, we need to divide both sides of the equation by -3 to isolate the variable $n$.

Q: Why do we divide both sides of the equation by -3?

A: We divide both sides of the equation by -3 to isolate the variable $n$. This allows us to express $n$ in terms of a single value.

Q: What is the final answer to the equation $-18 = -\frac{3}{2} n$?

A: The final answer to the equation $-18 = -\frac{3}{2} n$ is $n = 12$.

Q: Can I use this method to simplify other equations?

A: Yes, you can use this method to simplify other equations that involve fractions. The key is to multiply both sides of the equation by a common denominator to eliminate the fraction.

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

A: Some common mistakes to avoid when simplifying equations include forgetting to multiply or divide both sides of the equation by the same value, forgetting to check the sign of the constant when dividing both sides of the equation, and not checking the work by plugging the solution back into the original equation.

Q: How can I practice simplifying equations?

A: You can practice simplifying equations by working through examples and exercises. Start with simple equations and gradually move on to more complex ones. You can also use online resources and practice tests to help you improve your skills.

In conclusion, simplifying equations like $-18 = -\frac{3}{2} n$ is an important skill that has many real-world applications. By following the steps outlined in this article and practicing regularly, you can become proficient in simplifying equations and solving problems. Remember to always check your work and be mindful of common mistakes.

• When working with fractions, it's often helpful to multiply both sides of the equation by a common denominator to eliminate the fraction.
• When dividing both sides of the equation by a constant, make sure to check if the constant is positive or negative, as this can affect the sign of the result.
• Always check your work by plugging the solution back into the original equation to ensure that it is true.

Simplifying equations like $-18 = -\frac{3}{2} n$ has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, equations like this can be used to describe the motion of objects and predict their behavior. In engineering, equations like this can be used to design and optimize systems. In economics, equations like this can be used to model and analyze economic systems.

• One common mistake when simplifying equations is to forget to multiply or divide both sides of the equation by the same value.
• Another common mistake is to forget to check the sign of the constant when dividing both sides of the equation.
• A third common mistake is to not check the work by plugging the solution back into the original equation.

In conclusion, simplifying equations like $-18 = -\frac{3}{2} n$ is an important skill that has many real-world applications. By following the steps outlined in this article and practicing regularly, you can become proficient in simplifying equations and solving problems. Remember to always check your work and be mindful of common mistakes. With practice and patience, you will become proficient in simplifying equations and solving problems.