Question

Solve for
\[f\].
Give an exact answer.

\[9f=\dfrac{1}2\left(12f-2\right)\]
\[f =\]

Answer 1

To solve for \( f \) in the equation

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

we first eliminate the fraction by multiplying both sides by 2:

\[
2 \cdot 9f = 12f - 2.
\]

This simplifies to:

\[
18f = 12f - 2.
\]

Next, we will isolate \( f \) by moving the term \( 12f \) to the left side of the equation:

\[
18f - 12f = -2.
\]

This simplifies to:

\[
6f = -2.
\]

Now, divide both sides by 6 to solve for \( f \):

\[
f = \frac{-2}{6} = \frac{-1}{3}.
\]

Thus, the exact answer is

\[
\boxed{-\frac{1}{3}}.
\]