Solve for f 2f+2-f=6+3f-4f+6

$2 f + 2 - f = 6 + 3 f - 4 f + 6$

Step 1

Subtract $f$ from $2 f$ .

$f + 2 = 6 + 3 f - 4 f + 6$

Step 2

Simplify $6 + 3 f - 4 f + 6$ .

Add $6$ and $6$ .

$f + 2 = 3 f - 4 f + 12$

Subtract $4 f$ from $3 f$ .

$f + 2 = - f + 12$

Step 3

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

Add $f$ to both sides of the equation.

$f + 2 + f = 12$

Add $f$ and $f$ .

$2 f + 2 = 12$

Step 4

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

Subtract $2$ from both sides of the equation.

$2 f = 12 - 2$

Subtract $2$ from $12$ .

$2 f = 10$

Step 5

Divide each term in $2 f = 10$ by $2$ and simplify.

Divide each term in $2 f = 10$ by $2$ .

$\frac{2 f}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 f}{2} = \frac{10}{2}$

Divide $f$ by $1$ .

$f = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$f = 5$