Solve For { X $} : : : { \frac{2}{7}(4x - 18) = 12 \}

$$$$

Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving a linear equation involving fractions, specifically the equation $\frac{2}{7}(4x - 18) = 12$. We will break down the steps to solve this equation and provide a clear explanation of each step.

Step 1: Distribute the Fraction

To solve the equation, we need to start by distributing the fraction $\frac{2}{7}$ to the terms inside the parentheses. This means multiplying the fraction by each term inside the parentheses.

$\frac{2}{7}(4x - 18) = 12$

Distributing the fraction, we get:

$\frac{2}{7} \cdot 4x - \frac{2}{7} \cdot 18 = 12$

Step 2: Simplify the Equation

Now that we have distributed the fraction, we can simplify the equation by combining like terms.

$\frac{2}{7} \cdot 4x - \frac{2}{7} \cdot 18 = 12$

Simplifying, we get:

$\frac{8}{7}x - \frac{36}{7} = 12$

Step 3: Get Rid of the Fraction

To get rid of the fraction, we can multiply both sides of the equation by the denominator, which is 7.

$\frac{8}{7}x - \frac{36}{7} = 12$

Multiplying both sides by 7, we get:

$8x - 36 = 84$

Step 4: Add 36 to Both Sides

Now that we have eliminated the fraction, we can add 36 to both sides of the equation to isolate the term with the variable.

$8x - 36 = 84$

Adding 36 to both sides, we get:

$8x = 120$

Step 5: Divide Both Sides by 8

Finally, we can divide both sides of the equation by 8 to solve for x.

$8x = 120$

Dividing both sides by 8, we get:

$x = 15$

Conclusion

In this article, we solved the linear equation $\frac{2}{7}(4x - 18) = 12$ by distributing the fraction, simplifying the equation, getting rid of the fraction, adding 36 to both sides, and finally dividing both sides by 8. We found that the solution to the equation is x = 15.

Tips and Tricks

• When solving linear equations involving fractions, it's essential to distribute the fraction to the terms inside the parentheses.
• Simplifying the equation by combining like terms can make it easier to solve.
• Getting rid of the fraction by multiplying both sides by the denominator can make the equation easier to work with.
• Adding or subtracting the same value to both sides of the equation can help isolate the term with the variable.
• Dividing both sides of the equation by a non-zero value can help solve for the variable.

Real-World Applications

Solving linear equations is a fundamental concept in mathematics, and it has numerous real-world applications. For example:

• In physics, linear equations are used to describe the motion of objects.
• In economics, linear equations are used to model the behavior of markets.
• In computer science, linear equations are used to solve systems of equations and optimize algorithms.

Final Thoughts

Solving linear equations is a crucial skill in mathematics, and it has numerous real-world applications. By following the steps outlined in this article, you can solve linear equations involving fractions and become more confident in your ability to solve mathematical problems. Remember to distribute the fraction, simplify the equation, get rid of the fraction, add or subtract the same value to both sides, and finally divide both sides by a non-zero value to solve for the variable.

$$$$

Introduction

In our previous article, we solved the linear equation $\frac{2}{7}(4x - 18) = 12$ by distributing the fraction, simplifying the equation, getting rid of the fraction, adding 36 to both sides, and finally dividing both sides by 8. We found that the solution to the equation is x = 15. In this article, we will answer some frequently asked questions about solving linear equations involving fractions.

Q: What is the first step in solving a linear equation involving fractions?

A: The first step in solving a linear equation involving fractions is to distribute the fraction to the terms inside the parentheses. This means multiplying the fraction by each term inside the parentheses.

Q: How do I simplify a linear equation involving fractions?

A: To simplify a linear equation involving fractions, you can combine like terms. This means adding or subtracting terms that have the same variable and coefficient.

Q: How do I get rid of a fraction in a linear equation?

A: To get rid of a fraction in a linear equation, you can multiply both sides of the equation by the denominator. This will eliminate the fraction and make the equation easier to work with.

Q: What is the difference between adding and subtracting the same value to both sides of an equation?

A: Adding and subtracting the same value to both sides of an equation are two different operations. Adding the same value to both sides of an equation will not change the equation, while subtracting the same value from both sides of an equation will change the equation.

Q: How do I solve for the variable in a linear equation?

A: To solve for the variable in a linear equation, you can divide both sides of the equation by a non-zero value. This will isolate the variable and give you the solution to the equation.

Q: What are some real-world applications of solving linear equations?

A: Solving linear equations has numerous real-world applications, including physics, economics, and computer science. In physics, linear equations are used to describe the motion of objects. In economics, linear equations are used to model the behavior of markets. In computer science, linear equations are used to solve systems of equations and optimize algorithms.

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

A: Some common mistakes to avoid when solving linear equations include:

• Not distributing the fraction to the terms inside the parentheses
• Not simplifying the equation by combining like terms
• Not getting rid of the fraction by multiplying both sides by the denominator
• Not adding or subtracting the same value to both sides of the equation
• Not dividing both sides of the equation by a non-zero value

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through examples and exercises. You can also use online resources, such as math websites and apps, to practice solving linear equations.

Q: What are some tips for solving linear equations?

A: Some tips for solving linear equations include:

• Read the equation carefully and understand what is being asked
• Use the distributive property to distribute the fraction to the terms inside the parentheses
• Simplify the equation by combining like terms
• Get rid of the fraction by multiplying both sides by the denominator
• Add or subtract the same value to both sides of the equation
• Divide both sides of the equation by a non-zero value

Conclusion

Solving linear equations is a crucial skill in mathematics, and it has numerous real-world applications. By following the steps outlined in this article, you can solve linear equations involving fractions and become more confident in your ability to solve mathematical problems. Remember to distribute the fraction, simplify the equation, get rid of the fraction, add or subtract the same value to both sides, and finally divide both sides by a non-zero value to solve for the variable.