Solve for h f=1/4(g+h-k)

$f = \frac{1}{4} (g + h - k)$

Step 1

Rewrite the equation as $\frac{1}{4} \cdot (g + h - k) = f$ .

$\frac{1}{4} \cdot (g + h - k) = f$

Step 2

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cdot (g + h - k)) = 4 f$

Step 3

Simplify the left side.

Simplify $4 (\frac{1}{4} \cdot (g + h - k))$ .

Apply the distributive property.

$4 (\frac{1}{4} g + \frac{1}{4} h + \frac{1}{4} (- k)) = 4 f$

Simplify.

Combine $\frac{1}{4}$ and $g$ .

$4 (\frac{g}{4} + \frac{1}{4} h + \frac{1}{4} (- k)) = 4 f$

Combine $\frac{1}{4}$ and $h$ .

$4 (\frac{g}{4} + \frac{h}{4} + \frac{1}{4} (- k)) = 4 f$

Combine $\frac{1}{4}$ and $k$ .

$4 (\frac{g}{4} + \frac{h}{4} - \frac{k}{4}) = 4 f$

Apply the distributive property.

$4 \frac{g}{4} + 4 \frac{h}{4} + 4 (- \frac{k}{4}) = 4 f$

Simplify.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{g}{4} + 4 \frac{h}{4} + 4 (- \frac{k}{4}) = 4 f$

Rewrite the expression.

$g + 4 \frac{h}{4} + 4 (- \frac{k}{4}) = 4 f$

Cancel the common factor of $4$ .

Cancel the common factor.

$g + 4 \frac{h}{4} + 4 (- \frac{k}{4}) = 4 f$

Rewrite the expression.

$g + h + 4 (- \frac{k}{4}) = 4 f$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{k}{4}$ into the numerator.

$g + h + 4 \frac{- k}{4} = 4 f$

Cancel the common factor.

$g + h + 4 \frac{- k}{4} = 4 f$

Rewrite the expression.

$g + h - k = 4 f$

Step 4

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

Subtract $g$ from both sides of the equation.

$h - k = 4 f - g$

Add $k$ to both sides of the equation.

$h = 4 f - g + k$