Linear Equations in Two Variables

Oct 13, 2025 by pynkocean.com 74 views

Solving for f in the Equation 6f + 9g = 3g + f

Understanding the Equation

The given equation is 6f + 9g = 3g + f. To solve for f, we need to isolate the variable f on one side of the equation. This involves simplifying the equation and using algebraic techniques to isolate f.

Step 1: Simplify the Equation

The first step is to simplify the equation by combining like terms. We can start by subtracting 3g from both sides of the equation:

6f + 9g - 3g = 3g - 3g + f

This simplifies to:

6f + 6g = f

Step 2: Isolate f

Next, we need to isolate f on one side of the equation. We can do this by subtracting f from both sides of the equation:

6f - f + 6g = f - f

This simplifies to:

5f + 6g = 0

Step 3: Solve for f

Now, we need to solve for f. We can do this by subtracting 6g from both sides of the equation:

5f = -6g

Next, we can divide both sides of the equation by 5:

f = -6g/5

Conclusion

Therefore, the solution to the equation 6f + 9g = 3g + f is f = -6g/5.

Comparing the Solution to the Options

Let's compare the solution to the options:

A. f = -8g/3 B. f = -6g/5 C. f = -5g/6 D. f = 12g/7

The only option that matches the solution is option B: f = -6g/5.

Final Answer

The final answer is B. f = -6g/5.
Solving for f in the Equation 6f + 9g = 3g + f: Q&A

Q: What is the given equation?

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

Q: What is the goal of the problem?

A: The goal of the problem is to solve for f in the given equation.

Q: What steps are involved in solving for f?

A: The steps involved in solving for f are:

Simplifying the equation by combining like terms.
Isolating f on one side of the equation.
Solving for f.

Q: What is the first step in solving for f?

A: The first step in solving for f is to simplify the equation by combining like terms. This involves subtracting 3g from both sides of the equation.

Q: What is the result of simplifying the equation?

A: The result of simplifying the equation is 6f + 6g = f.

Q: What is the next step in solving for f?

A: The next step in solving for f is to isolate f on one side of the equation. This involves subtracting f from both sides of the equation.

Q: What is the result of isolating f?

A: The result of isolating f is 5f + 6g = 0.

Q: What is the final step in solving for f?

A: The final step in solving for f is to solve for f. This involves subtracting 6g from both sides of the equation and then dividing both sides of the equation by 5.

Q: What is the solution to the equation?

A: The solution to the equation is f = -6g/5.

Q: How does the solution compare to the options?

A: The solution f = -6g/5 matches option B.

Q: What is the final answer?

A: The final answer is B. f = -6g/5.

Frequently Asked Questions

Q: What is the equation 6f + 9g = 3g + f? A: The equation 6f + 9g = 3g + f is a linear equation in two variables, f and g.
Q: How do I solve for f in the equation 6f + 9g = 3g + f? A: To solve for f, you need to simplify the equation by combining like terms, isolate f on one side of the equation, and then solve for f.
Q: What is the solution to the equation 6f + 9g = 3g + f? A: The solution to the equation 6f + 9g = 3g + f is f = -6g/5.

Related Topics

Solving Linear Equations
Algebraic Techniques
Linear Equations in Two Variables

Conclusion

Solving for f in the equation 6f + 9g = 3g + f involves simplifying the equation, isolating f, and then solving for f. The solution to the equation is f = -6g/5, which matches option B.