https://file.aiquickdraw.com/mathbot/file/17269676967146qbdimlh.jpg

The equation provided in the image is:

\[ 9f = \frac{1}{2}(12f - 2) \]

To solve for \( f \), we'll first distribute the \( \frac{1}{2} \) on the right side of the equation:

\[ 9f = \frac{1}{2} \times 12f - \frac{1}{2} \times 2 \]

This simplifies to:

\[ 9f = 6f - 1 \]

Next, we subtract \( 6f \) from both sides to get:

\[ 3f = -1 \]

Finally, we divide both sides by 3 to isolate \( f \):

\[ f = -\frac{1}{3} \]

So, \( f = -\frac{1}{3} \).

Would you like to know more details or have any questions about this solution? Here are some related questions you might find interesting:
1. What happens if you multiply both sides of the original equation by 2 first?
2. How would the solution change if the equation were \( 9f = \frac{1}{2}(12f + 2) \)?
3. Can you graph the equation \( 9f = \frac{1}{2}(12f - 2) \) to visualize the solution?
4. What is the significance of the coefficients 9 and 12 in this equation?
5. What are the steps to check if \( f = -\frac{1}{3} \) is indeed a correct solution?

**Tip**: When solving equations, always aim to simplify one side and get all the variable terms on one side and the constants on the other to isolate the variable.

Learn how to solve the linear equation 9f = (1/2)(12f - 2) with a step-by-step breakdown. This problem involves using algebraic methods such as distribution and variable isolation. Perfect for students in Grades 8-10.

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