Solve for h f=1/5(g+h-k)

$f = \frac{1}{5} (g + h - k)$

Step 1

Rewrite the equation as $\frac{1}{5} \cdot (g + h - k) = f$ .

$\frac{1}{5} \cdot (g + h - k) = f$

Step 2

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} \cdot (g + h - k)) = 5 f$

Step 3

Simplify the left side.

Simplify $5 (\frac{1}{5} \cdot (g + h - k))$ .

Apply the distributive property.

$5 (\frac{1}{5} g + \frac{1}{5} h + \frac{1}{5} (- k)) = 5 f$

Simplify.

Combine $\frac{1}{5}$ and $g$ .

$5 (\frac{g}{5} + \frac{1}{5} h + \frac{1}{5} (- k)) = 5 f$

Combine $\frac{1}{5}$ and $h$ .

$5 (\frac{g}{5} + \frac{h}{5} + \frac{1}{5} (- k)) = 5 f$

Combine $\frac{1}{5}$ and $k$ .

$5 (\frac{g}{5} + \frac{h}{5} - \frac{k}{5}) = 5 f$

Apply the distributive property.

$5 \frac{g}{5} + 5 \frac{h}{5} + 5 (- \frac{k}{5}) = 5 f$

Simplify.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{g}{5} + 5 \frac{h}{5} + 5 (- \frac{k}{5}) = 5 f$

Rewrite the expression.

$g + 5 \frac{h}{5} + 5 (- \frac{k}{5}) = 5 f$

Cancel the common factor of $5$ .

Cancel the common factor.

$g + 5 \frac{h}{5} + 5 (- \frac{k}{5}) = 5 f$

Rewrite the expression.

$g + h + 5 (- \frac{k}{5}) = 5 f$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{k}{5}$ into the numerator.

$g + h + 5 \frac{- k}{5} = 5 f$

Cancel the common factor.

$g + h + 5 \frac{- k}{5} = 5 f$

Rewrite the expression.

$g + h - k = 5 f$

Step 4

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

Subtract $g$ from both sides of the equation.

$h - k = 5 f - g$

Add $k$ to both sides of the equation.

$h = 5 f - g + k$