Solve For The Missing Value In The Equation:$\[ \frac{2}{3x} = \frac{\square}{18x^7} \\]

**Solve for the Missing Value in the Equation: A Step-by-Step Guide** ===========================================================

Introduction

In this article, we will delve into the world of algebra and solve for the missing value in a given equation. The equation in question is $\frac{2}{3x} = \frac{\square}{18x^7}$. We will break down the solution into manageable steps, making it easy to follow and understand.

What is Algebra?

Algebra is a branch of mathematics that deals with the study of variables and their relationships. It involves solving equations and manipulating expressions to find the value of unknown variables. Algebra is a fundamental subject that has numerous applications in various fields, including science, engineering, economics, and more.

Understanding the Given Equation

The given equation is $\frac{2}{3x} = \frac{\square}{18x^7}$. This equation involves fractions, variables, and exponents. To solve for the missing value, we need to isolate the variable and simplify the equation.

Step 1: Multiply Both Sides by the Denominator

To eliminate the fractions, we can multiply both sides of the equation by the denominators. In this case, the denominators are $3x$ and $18x^7$. Multiplying both sides by $3x \cdot 18x^7$ will eliminate the fractions.

\frac{2}{3x} \cdot 3x \cdot 18x^7 = \frac{\square}{18x^7} \cdot 3x \cdot 18x^7

Step 2: Simplify the Equation

After multiplying both sides by the denominators, we can simplify the equation. The left-hand side becomes $2 \cdot 18x^7$, and the right-hand side becomes $\square \cdot 3x \cdot 18x^7$.

2 \cdot 18x^7 = \square \cdot 3x \cdot 18x^7

Step 3: Divide Both Sides by the Common Factor

To isolate the variable, we can divide both sides of the equation by the common factor. In this case, the common factor is $18x^7$. Dividing both sides by $18x^7$ will isolate the variable.

\frac{2 \cdot 18x^7}{18x^7} = \frac{\square \cdot 3x \cdot 18x^7}{18x^7}

Step 4: Simplify the Equation

After dividing both sides by the common factor, we can simplify the equation. The left-hand side becomes $2$, and the right-hand side becomes $\square \cdot 3x$.

2 = \square \cdot 3x

Step 5: Solve for the Missing Value

To solve for the missing value, we can divide both sides of the equation by $3x$. This will isolate the variable and give us the value of the missing value.

\frac{2}{3x} = \square

Conclusion

In this article, we solved for the missing value in the equation $\frac{2}{3x} = \frac{\square}{18x^7}$. We broke down the solution into manageable steps, making it easy to follow and understand. By multiplying both sides by the denominators, simplifying the equation, dividing both sides by the common factor, and solving for the missing value, we were able to find the value of the missing value.

Frequently Asked Questions

Q: What is the missing value in the equation?

A: The missing value in the equation is $\square$.

Q: How do I solve for the missing value?

A: To solve for the missing value, you can multiply both sides of the equation by the denominators, simplify the equation, divide both sides by the common factor, and solve for the missing value.

Q: What is the value of the missing value?

A: The value of the missing value is $\frac{2}{3x}$.

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

A: Yes, you can use this method to solve other equations involving fractions, variables, and exponents.

Q: What is the importance of algebra in real-life applications?

A: Algebra is a fundamental subject that has numerous applications in various fields, including science, engineering, economics, and more. It is used to model real-world problems, make predictions, and optimize solutions.

Q: How can I practice solving equations?

A: You can practice solving equations by working on problems and exercises, using online resources, and seeking help from teachers or tutors.