Solve For { K $}$ In The Equation:${ \frac{5}{k} = \frac{2}{k-4} }$

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$. This equation involves fractions and variables, making it a bit more challenging to solve. However, with the right approach and techniques, we can easily find the value of ${ k }$.

Understanding the Equation

The given equation is ${\frac{5}{k} = \frac{2}{k-4}}$. This equation involves two fractions with variables in the denominators. To solve for ${ k }$, we need to eliminate the fractions and isolate the variable. The first step is to cross-multiply the fractions, which means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.

Cross-Multiplying the Fractions

To cross-multiply the fractions, we multiply the numerator of the first fraction by the denominator of the second fraction and vice versa. This gives us:

${5(k-4) = 2k}$

Expanding and Simplifying the Equation

Now that we have cross-multiplied the fractions, we need to expand and simplify the equation. To do this, we need to distribute the 5 to the terms inside the parentheses and combine like terms.

${5k - 20 = 2k}$

Isolating the Variable

The next step is to isolate the variable ${ k }$. To do this, we need to get all the terms with ${ k }$ on one side of the equation and the constant terms on the other side. We can do this by subtracting ${ 2k }$ from both sides of the equation.

${5k - 2k - 20 = 2k - 2k}$

Simplifying the Equation

Now that we have isolated the variable, we can simplify the equation by combining like terms.

${3k - 20 = 0}$

Adding 20 to Both Sides

The next step is to add 20 to both sides of the equation to isolate the term with ${ k }$.

${3k - 20 + 20 = 0 + 20}$

Simplifying the Equation

Now that we have added 20 to both sides of the equation, we can simplify the equation by combining like terms.

${3k = 20}$

Dividing Both Sides by 3

The final step is to divide both sides of the equation by 3 to solve for ${ k }$.

${\frac{3k}{3} = \frac{20}{3}}$

Simplifying the Equation

Now that we have divided both sides of the equation by 3, we can simplify the equation by combining like terms.

${k = \frac{20}{3}}$

Conclusion

In this article, we have solved for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$. We started by cross-multiplying the fractions, expanding and simplifying the equation, isolating the variable, and finally solving for ${ k }$. The final solution is ${ k = \frac{20}{3} }$.

Final Answer

The final answer is ${ k = \frac{20}{3} }$.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Cross-multiply the fractions: ${5(k-4) = 2k}$
2. Expand and simplify the equation: ${5k - 20 = 2k}$
3. Isolate the variable: ${5k - 2k - 20 = 2k - 2k}$
4. Simplify the equation: ${3k - 20 = 0}$
5. Add 20 to both sides: ${3k - 20 + 20 = 0 + 20}$
6. Simplify the equation: ${3k = 20}$
7. Divide both sides by 3: ${\frac{3k}{3} = \frac{20}{3}}$
8. Simplify the equation: ${k = \frac{20}{3}}$

Frequently Asked Questions

• What is the value of ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?
• How do we solve for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?
• What is the step-by-step solution to the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

Answer to Frequently Asked Questions

• The value of ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$ is ${ k = \frac{20}{3} }$.
• To solve for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$, we need to cross-multiply the fractions, expand and simplify the equation, isolate the variable, and finally solve for ${ k }$.
• The step-by-step solution to the equation ${\frac{5}{k} = \frac{2}{k-4}}$ is as follows:
  1. Cross-multiply the fractions: ${5(k-4) = 2k}$
  2. Expand and simplify the equation: ${5k - 20 = 2k}$
  3. Isolate the variable: ${5k - 2k - 20 = 2k - 2k}$
  4. Simplify the equation: ${3k - 20 = 0}$
  5. Add 20 to both sides: ${3k - 20 + 20 = 0 + 20}$
  6. Simplify the equation: ${3k = 20}$
  7. Divide both sides by 3: ${\frac{3k}{3} = \frac{20}{3}}$
  8. Simplify the equation: ${k = \frac{20}{3}}$
     

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Introduction

In our previous article, we solved for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$. We used various techniques such as cross-multiplying, expanding and simplifying, isolating the variable, and finally solving for ${ k }$. In this article, we will answer some frequently asked questions related to solving for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$.

Q&A

Q: What is the value of ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

A: The value of ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$ is ${ k = \frac{20}{3} }$.

Q: How do we solve for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

A: To solve for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$, we need to cross-multiply the fractions, expand and simplify the equation, isolate the variable, and finally solve for ${ k }$.

Q: What is the step-by-step solution to the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

A: The step-by-step solution to the equation ${\frac{5}{k} = \frac{2}{k-4}}$ is as follows: 1. Cross-multiply the fractions: ${5(k-4) = 2k}$ 2. Expand and simplify the equation: ${5k - 20 = 2k}$ 3. Isolate the variable: ${5k - 2k - 20 = 2k - 2k}$ 4. Simplify the equation: ${3k - 20 = 0}$ 5. Add 20 to both sides: ${3k - 20 + 20 = 0 + 20}$ 6. Simplify the equation: ${3k = 20}$ 7. Divide both sides by 3: ${\frac{3k}{3} = \frac{20}{3}}$ 8. Simplify the equation: ${k = \frac{20}{3}}$

Q: What are some common mistakes to avoid when solving for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

A: Some common mistakes to avoid when solving for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$ include: * Not cross-multiplying the fractions * Not expanding and simplifying the equation * Not isolating the variable * Not solving for ${ k }$ correctly

Q: How do we check our solution for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

A: To check our solution for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$, we can plug the value of ${ k }$ back into the original equation and see if it is true.

Q: What are some real-world applications of solving for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

A: Some real-world applications of solving for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$ include: * Finding the value of a variable in a mathematical model * Solving a problem in physics or engineering * Finding the solution to a system of equations

Conclusion

In this article, we have answered some frequently asked questions related to solving for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$. We have covered topics such as the value of ${ k }$, the step-by-step solution, common mistakes to avoid, and real-world applications. We hope that this article has been helpful in understanding how to solve for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$.

Final Answer

The final answer is ${ k = \frac{20}{3} }$.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Cross-multiply the fractions: ${5(k-4) = 2k}$
2. Expand and simplify the equation: ${5k - 20 = 2k}$
3. Isolate the variable: ${5k - 2k - 20 = 2k - 2k}$
4. Simplify the equation: ${3k - 20 = 0}$
5. Add 20 to both sides: ${3k - 20 + 20 = 0 + 20}$
6. Simplify the equation: ${3k = 20}$
7. Divide both sides by 3: ${\frac{3k}{3} = \frac{20}{3}}$
8. Simplify the equation: ${k = \frac{20}{3}}$

Frequently Asked Questions

• What is the value of ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?
• How do we solve for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$?
• What is the step-by-step solution to the equation ${\frac{5}{k} = \frac{2}{k-4}}$?

Answer to Frequently Asked Questions

• The value of ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$ is ${ k = \frac{20}{3} }$.
• To solve for ${ k }$ in the equation ${\frac{5}{k} = \frac{2}{k-4}}$, we need to cross-multiply the fractions, expand and simplify the equation, isolate the variable, and finally solve for ${ k }$.
• The step-by-step solution to the equation ${\frac{5}{k} = \frac{2}{k-4}}$ is as follows:
  1. Cross-multiply the fractions: ${5(k-4) = 2k}$
  2. Expand and simplify the equation: ${5k - 20 = 2k}$
  3. Isolate the variable: ${5k - 2k - 20 = 2k - 2k}$
  4. Simplify the equation: ${3k - 20 = 0}$
  5. Add 20 to both sides: ${3k - 20 + 20 = 0 + 20}$
  6. Simplify the equation: ${3k = 20}$
  7. Divide both sides by 3: ${\frac{3k}{3} = \frac{20}{3}}$
  8. Simplify the equation: ${k = \frac{20}{3}}$