Solve for f 1/2(6-2f)=6

$\frac{1}{2} (6 - 2 f) = 6$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (6 - 2 f)) = 2 \cdot 6$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (6 - 2 f))$ .

Apply the distributive property.

$2 (\frac{1}{2} \cdot 6 + \frac{1}{2} (- 2 f)) = 2 \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 (\frac{1}{2} \cdot (2 (3)) + \frac{1}{2} (- 2 f)) = 2 \cdot 6$

Cancel the common factor.

$2 (\frac{1}{2} \cdot (2 \cdot 3) + \frac{1}{2} (- 2 f)) = 2 \cdot 6$

Rewrite the expression.

$2 (3 + \frac{1}{2} (- 2 f)) = 2 \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 f$ .

$2 (3 + \frac{1}{2} (2 (- f))) = 2 \cdot 6$

Cancel the common factor.

$2 (3 + \frac{1}{2} (2 (- f))) = 2 \cdot 6$

Rewrite the expression.

$2 (3 - f) = 2 \cdot 6$

Apply the distributive property.

$2 \cdot 3 + 2 (- f) = 2 \cdot 6$

Multiply.

Multiply $2$ by $3$ .

$6 + 2 (- f) = 2 \cdot 6$

Multiply $- 1$ by $2$ .

$6 - 2 f = 2 \cdot 6$

Simplify the right side.

Multiply $2$ by $6$ .

$6 - 2 f = 12$

Step 3

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

Subtract $6$ from both sides of the equation.

$- 2 f = 12 - 6$

Subtract $6$ from $12$ .

$- 2 f = 6$

Step 4

Divide each term in $- 2 f = 6$ by $- 2$ and simplify.

Divide each term in $- 2 f = 6$ by $- 2$ .

$\frac{- 2 f}{- 2} = \frac{6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 f}{- 2} = \frac{6}{- 2}$

Divide $f$ by $1$ .

$f = \frac{6}{- 2}$

Simplify the right side.

Divide $6$ by $- 2$ .

$f = - 3$

Solve for f 1/2(6-2f)=6

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