Solve The Equation: X 7 = 18 21 \frac{x}{7}=\frac{18}{21} 7 X ​ = 21 18 ​

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Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used to solve problems, make predictions, and understand the world around us. One of the most important concepts in mathematics is algebra, which deals with the study of variables and their relationships. In this article, we will focus on solving a simple equation involving fractions, specifically the equation $\frac{x}{7}=\frac{18}{21}$.

Understanding the Equation

The given equation is a simple linear equation involving fractions. The equation states that the ratio of $x$ to $7$ is equal to the ratio of $18$ to $21$. To solve this equation, we need to isolate the variable $x$ and find its value.

Step 1: Simplify the Fractions

The first step in solving the equation is to simplify the fractions. We can simplify the fraction $\frac{18}{21}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$. This gives us $\frac{6}{7}$.

import math
numerator = 18
denominator = 21

gcd = math.gcd(numerator, denominator)

simplified_numerator = numerator // gcd
simplified_denominator = denominator // gcd
print(f"The simplified fraction is {simplified_numerator}/{simplified_denominator}")

Step 2: Cross-Multiply

Now that we have simplified the fraction, we can cross-multiply to get rid of the fractions. Cross-multiplying involves multiplying both sides of the equation by the denominators of the fractions. In this case, we multiply both sides by $7$.

# Define the variables
x = None
equation = "x/7 = 6/7"

x = 6 * 7
print(f"The value of x is {x}")

Step 3: Solve for x

Now that we have cross-multiplied, we can solve for $x$. We can do this by dividing both sides of the equation by $7$.

# Define the variables
x = None
equation = "6*7 = x"

x = 6 * 7
print(f"The value of x is {x}")

Conclusion

In this article, we solved the equation $\frac{x}{7}=\frac{18}{21}$ using the steps of simplifying the fractions, cross-multiplying, and solving for $x$. We used Python code to demonstrate each step and make the solution more accessible. The final value of $x$ is $42$.

Final Answer

The final answer is $\boxed{42}$.

Related Topics

• Solving linear equations
• Simplifying fractions
• Cross-multiplying
• Algebraic manipulations

Further Reading

• Khan Academy: Solving Linear Equations
• Mathway: Simplifying Fractions
• Wolfram Alpha: Cross-Multiplying

References

• [1] "Algebra" by Michael Artin
• [2] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
• [3] "Introduction to Algebra" by Richard Rusczyk
  

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Introduction

In our previous article, we solved the equation $\frac{x}{7}=\frac{18}{21}$ using the steps of simplifying the fractions, cross-multiplying, and solving for $x$. In this article, we will answer some frequently asked questions (FAQs) related to solving this equation.

Q: What is the greatest common divisor (GCD) of 18 and 21?

A: The greatest common divisor (GCD) of 18 and 21 is 3.

Q: Why do we need to simplify the fractions?

A: We need to simplify the fractions to make the equation easier to solve. Simplifying the fractions involves dividing both the numerator and the denominator by their greatest common divisor.

Q: What is cross-multiplication?

A: Cross-multiplication is a technique used to get rid of the fractions in an equation. It involves multiplying both sides of the equation by the denominators of the fractions.

Q: How do we solve for x?

A: To solve for x, we need to isolate the variable x on one side of the equation. We can do this by dividing both sides of the equation by the coefficient of x.

Q: What is the final value of x?

A: The final value of x is 42.

Q: Can we use a calculator to solve this equation?

A: Yes, we can use a calculator to solve this equation. However, it's always a good idea to understand the steps involved in solving the equation.

Q: What are some common mistakes to avoid when solving this equation?

A: Some common mistakes to avoid when solving this equation include:

• Not simplifying the fractions
• Not cross-multiplying
• Not isolating the variable x
• Not checking the solution

Q: How do we check the solution?

A: To check the solution, we need to plug the value of x back into the original equation and make sure it's true.

Q: What are some real-world applications of solving this equation?

A: Solving this equation has many real-world applications, including:

• Calculating the area of a rectangle
• Finding the volume of a cube
• Determining the cost of a product

Q: Can we use this equation to solve other types of problems?

A: Yes, we can use this equation to solve other types of problems, including:

• Solving linear equations with fractions
• Solving quadratic equations
• Solving systems of equations

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to solving the equation $\frac{x}{7}=\frac{18}{21}$. We covered topics such as simplifying fractions, cross-multiplying, and solving for x. We also discussed some common mistakes to avoid and how to check the solution.

Final Answer

The final answer is $\boxed{42}$.

Related Topics

• Solving linear equations
• Simplifying fractions
• Cross-multiplying
• Algebraic manipulations

Further Reading

• Khan Academy: Solving Linear Equations
• Mathway: Simplifying Fractions
• Wolfram Alpha: Cross-Multiplying

References

• [1] "Algebra" by Michael Artin
• [2] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
• [3] "Introduction to Algebra" by Richard Rusczyk