Solve For F F F In The Equation:${6f + 9g = 3g + F}$A. F = − 8 G 3 F = \frac{-8g}{3} F = 3 − 8 G ​ B. F = − 6 G 5 F = \frac{-6g}{5} F = 5 − 6 G ​ C. F = − 5 G 6 F = \frac{-5g}{6} F = 6 − 5 G ​ D. F = 12 G 7 F = \frac{12g}{7} F = 7 12 G ​

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Introduction

In this article, we will be solving for the variable ff in a given linear equation. The equation is 6f+9g=3g+f6f + 9g = 3g + f. We will use algebraic manipulation to isolate the variable ff and find its value in terms of gg.

The Given Equation

The given equation is 6f+9g=3g+f6f + 9g = 3g + f. Our goal is to solve for ff in this equation.

Step 1: Subtract ff from Both Sides

To start solving for ff, we will subtract ff from both sides of the equation. This will help us isolate the term containing ff.

6f−f+9g=3g+f−f{6f - f + 9g = 3g + f - f}

This simplifies to:

5f+9g=3g{5f + 9g = 3g}

Step 2: Subtract 9g9g from Both Sides

Next, we will subtract 9g9g from both sides of the equation. This will help us eliminate the term containing gg.

5f+9g−9g=3g−9g{5f + 9g - 9g = 3g - 9g}

This simplifies to:

5f=−6g{5f = -6g}

Step 3: Divide Both Sides by 5

Finally, we will divide both sides of the equation by 5 to solve for ff.

5f5=−6g5{\frac{5f}{5} = \frac{-6g}{5}}

This simplifies to:

f=−6g5{f = \frac{-6g}{5}}

Conclusion

We have successfully solved for the variable ff in the given equation. The value of ff in terms of gg is f=−6g5f = \frac{-6g}{5}.

Comparison with Answer Choices

Let's compare our solution with the answer choices provided.

  • A. f=−8g3f = \frac{-8g}{3}: This is not equal to our solution.
  • B. f=−6g5f = \frac{-6g}{5}: This is equal to our solution.
  • C. f=−5g6f = \frac{-5g}{6}: This is not equal to our solution.
  • D. f=12g7f = \frac{12g}{7}: This is not equal to our solution.

Therefore, the correct answer is B. f=−6g5f = \frac{-6g}{5}.

Final Answer

The final answer is B\boxed{B}

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Introduction

In our previous article, we solved for the variable ff in the given linear equation 6f+9g=3g+f6f + 9g = 3g + f. We used algebraic manipulation to isolate the variable ff and find its value in terms of gg. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information.

Q&A

Q: What is the given equation?

A: The given equation is 6f+9g=3g+f6f + 9g = 3g + f.

Q: How do we start solving for ff?

A: To start solving for ff, we will subtract ff from both sides of the equation. This will help us isolate the term containing ff.

Q: What is the result of subtracting ff from both sides?

A: The result of subtracting ff from both sides is 5f+9g=3g5f + 9g = 3g.

Q: How do we eliminate the term containing gg?

A: We will subtract 9g9g from both sides of the equation to eliminate the term containing gg.

Q: What is the result of subtracting 9g9g from both sides?

A: The result of subtracting 9g9g from both sides is 5f=−6g5f = -6g.

Q: How do we solve for ff?

A: We will divide both sides of the equation by 5 to solve for ff.

Q: What is the final result?

A: The final result is f=−6g5f = \frac{-6g}{5}.

Q: How do we compare our solution with the answer choices?

A: We will compare our solution with the answer choices provided to determine the correct answer.

Q: What is the correct answer?

A: The correct answer is B. f=−6g5f = \frac{-6g}{5}.

Additional Tips and Tricks

Tip 1: Pay Attention to the Signs

When solving for ff, pay attention to the signs of the terms. In this case, we had to subtract ff from both sides, which resulted in a negative sign in front of the term containing gg.

Tip 2: Use Algebraic Manipulation

Algebraic manipulation is a powerful tool for solving equations. In this case, we used subtraction and division to isolate the variable ff.

Tip 3: Check Your Work

Always check your work to ensure that you have solved the equation correctly. In this case, we compared our solution with the answer choices to determine the correct answer.

Conclusion

Solving for ff in the given equation requires careful algebraic manipulation and attention to the signs of the terms. By following the steps outlined in this article, you can solve for ff and determine the correct answer.

Final Answer

The final answer is B\boxed{B}