\( y=\frac{f+4 x}{7+f x} \) find \( x \) \( x=\square \)

To solve for \( x \) in the equation \( y=\frac{f+4 x}{7+f x} \), we first cross-multiply to eliminate the fraction: \[ y(7 + f x) = f + 4 x. \] Expanding this gives us: \[ 7y + yfx = f + 4x. \] Now, let's collect the terms involving \( x \) on one side: \[ yfx - 4x = f - 7y. \] Factor \( x \) from the left side: \[ x(yf - 4) = f - 7y. \] Now, solve for \( x \): \[ x = \frac{f - 7y}{yf - 4}. \] And there you have it! So, \( x = \frac{f - 7y}{yf - 4} \).