Solve for f 8+5f=-4f+1+8f

$8 + 5 f = - 4 f + 1 + 8 f$

Step 1

Since $f$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 4 f + 1 + 8 f = 8 + 5 f$

Step 2

Add $- 4 f$ and $8 f$ .

$4 f + 1 = 8 + 5 f$

Step 3

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

Subtract $5 f$ from both sides of the equation.

$4 f + 1 - 5 f = 8$

Subtract $5 f$ from $4 f$ .

$- f + 1 = 8$

Step 4

Move all terms not containing $f$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$- f = 8 - 1$

Subtract $1$ from $8$ .

$- f = 7$

Step 5

Divide each term in $- f = 7$ by $- 1$ and simplify.

Divide each term in $- f = 7$ by $- 1$ .

$\frac{- f}{- 1} = \frac{7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{f}{1} = \frac{7}{- 1}$

Divide $f$ by $1$ .

$f = \frac{7}{- 1}$

Simplify the right side.

Divide $7$ by $- 1$ .

$f = - 7$