Solve for f 6f+2g=8f+9

$6 f + 2 g = 8 f + 9$

Move all terms containing $f$ to the left side of the equation.

Subtract $8 f$ from both sides of the equation.

$6 f + 2 g - 8 f = 9$

Subtract $8 f$ from $6 f$ .

$- 2 f + 2 g = 9$

Subtract $2 g$ from both sides of the equation.

$- 2 f = 9 - 2 g$

Divide each term in $- 2 f = 9 - 2 g$ by $- 2$ and simplify.

Divide each term in $- 2 f = 9 - 2 g$ by $- 2$ .

$\frac{- 2 f}{- 2} = \frac{9}{- 2} + \frac{- 2 g}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 f}{- 2} = \frac{9}{- 2} + \frac{- 2 g}{- 2}$

Divide $f$ by $1$ .

$f = \frac{9}{- 2} + \frac{- 2 g}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$f = - \frac{9}{2} + \frac{- 2 g}{- 2}$

Cancel the common factor of $- 2$ .

Cancel the common factor.

$f = - \frac{9}{2} + \frac{- 2 g}{- 2}$

Divide $g$ by $1$ .

$f = - \frac{9}{2} + g$