Solve For { K $} . . . { \frac{2}{3}(k+6) = 14 \} { K = $}$

Solving for k: A Step-by-Step Guide to Isolating the Variable

Introduction

In algebra, solving for a variable means finding the value of that variable that makes the equation true. In this article, we will focus on solving for the variable k in the given equation: $\frac{2}{3}(k+6) = 14$. We will break down the solution into manageable steps, making it easy to understand and follow along.

Step 1: Multiply Both Sides by 3 to Eliminate the Fraction

To start solving for k, we need to get rid of the fraction on the left-hand side of the equation. We can do this by multiplying both sides of the equation by 3, which is the denominator of the fraction. This will give us:

$$2(k+6) = 14 \times 3$$

By multiplying both sides by 3, we have eliminated the fraction and made the equation easier to work with.

Step 2: Distribute the 2 to the Terms Inside the Parentheses

Now that we have eliminated the fraction, we can distribute the 2 to the terms inside the parentheses. This means we multiply the 2 by each term inside the parentheses:

$$2k + 12 = 42$$

By distributing the 2, we have simplified the equation and made it easier to solve for k.

Step 3: Subtract 12 from Both Sides to Isolate the Term with k

To isolate the term with k, we need to get rid of the constant term on the left-hand side of the equation. We can do this by subtracting 12 from both sides of the equation:

$$2k = 42 - 12$$

By subtracting 12 from both sides, we have isolated the term with k and made it easier to solve for.

Step 4: Simplify the Right-Hand Side of the Equation

Now that we have isolated the term with k, we can simplify the right-hand side of the equation by subtracting 12 from 42:

$$2k = 30$$

By simplifying the right-hand side, we have made the equation easier to solve for k.

Step 5: Divide Both Sides by 2 to Solve for k

Finally, we can solve for k by dividing both sides of the equation by 2:

$$k = \frac{30}{2}$$

By dividing both sides by 2, we have found the value of k that makes the equation true.

Conclusion

In this article, we have solved for the variable k in the given equation: $\frac{2}{3}(k+6) = 14$. We broke down the solution into manageable steps, making it easy to understand and follow along. By multiplying both sides by 3, distributing the 2, subtracting 12, simplifying the right-hand side, and dividing both sides by 2, we found the value of k to be $\boxed{15}$.

Frequently Asked Questions

• What is the value of k in the equation $\frac{2}{3}(k+6) = 14$?
  • The value of k is $\boxed{15}$.
• How do I solve for k in an equation with a fraction?
  • To solve for k in an equation with a fraction, multiply both sides of the equation by the denominator of the fraction to eliminate the fraction.
• What is the first step in solving for k in an equation?
  • The first step in solving for k in an equation is to eliminate any fractions by multiplying both sides of the equation by the denominator of the fraction.

Additional Resources

• Algebra Tutorial: A comprehensive tutorial on algebra, including solving equations and inequalities.
• Mathematics Glossary: A glossary of mathematical terms, including definitions and examples.
• Practice Problems: A set of practice problems to help you improve your skills in solving equations and inequalities.
  Solving for k: A Q&A Article

Introduction

In our previous article, we solved for the variable k in the equation $\frac{2}{3}(k+6) = 14$. We broke down the solution into manageable steps, making it easy to understand and follow along. In this article, we will answer some frequently asked questions about solving for k in equations.

Q&A

Q: What is the first step in solving for k in an equation?

A: The first step in solving for k in an equation is to eliminate any fractions by multiplying both sides of the equation by the denominator of the fraction.

Q: How do I solve for k in an equation with a fraction?

A: To solve for k in an equation with a fraction, multiply both sides of the equation by the denominator of the fraction to eliminate the fraction. Then, distribute the resulting number to the terms inside the parentheses, and simplify the equation.

Q: What is the difference between solving for k and solving for x?

A: Solving for k and solving for x are essentially the same thing. The variable being solved for is simply a placeholder, and the steps to solve for it are the same regardless of the variable being used.

Q: Can I use the same steps to solve for k in an equation with a decimal?

A: Yes, you can use the same steps to solve for k in an equation with a decimal. However, you may need to use a calculator to perform the calculations.

Q: How do I know if I have solved for k correctly?

A: To check if you have solved for k correctly, plug the value of k back into the original equation and see if it is true. If the equation is true, then you have solved for k correctly.

Q: What if I get stuck while solving for k?

A: If you get stuck while solving for k, try breaking down the equation into smaller steps. Simplify the equation as much as possible, and then try to solve for k again. If you are still having trouble, try using a different method or seeking help from a teacher or tutor.

Tips and Tricks

• Read the equation carefully: Before starting to solve for k, read the equation carefully to make sure you understand what is being asked.
• Use a pencil: It's a good idea to use a pencil when solving for k, so you can easily erase any mistakes you make.
• Check your work: Always check your work by plugging the value of k back into the original equation.
• Practice, practice, practice: The more you practice solving for k, the more comfortable you will become with the steps and the easier it will be to solve for k.

Common Mistakes to Avoid

• Forgetting to multiply both sides by the denominator: Make sure to multiply both sides of the equation by the denominator of the fraction to eliminate the fraction.
• Not distributing the resulting number: Make sure to distribute the resulting number to the terms inside the parentheses.
• Not simplifying the equation: Make sure to simplify the equation as much as possible before solving for k.
• Not checking your work: Always check your work by plugging the value of k back into the original equation.

Conclusion

Solving for k in equations can be a challenging task, but with practice and patience, you can become proficient in solving for k. Remember to read the equation carefully, use a pencil, check your work, and practice, practice, practice. By following these tips and avoiding common mistakes, you will be well on your way to becoming a master of solving for k.