Solve f=1/9(g+h-k)

$$f = \frac { 1 } { 9 } ( g + h - k )$$

Solve for g

$$g=9f-h+k$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{9} by g+h-k.

$$f=\frac{1}{9}g+\frac{1}{9}h-\frac{1}{9}k$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{9}g+\frac{1}{9}h-\frac{1}{9}k=f$$

Subtract \frac{1}{9}h from both sides.

$$\frac{1}{9}g-\frac{1}{9}k=f-\frac{1}{9}h$$

Add \frac{1}{9}k to both sides.

$$\frac{1}{9}g=f-\frac{1}{9}h+\frac{1}{9}k$$

The equation is in standard form.

$$\frac{1}{9}g=\frac{k}{9}-\frac{h}{9}+f$$

Multiply both sides by 9.

$$\frac{\frac{1}{9}g}{\frac{1}{9}}=\frac{\frac{k}{9}-\frac{h}{9}+f}{\frac{1}{9}}$$

Dividing by \frac{1}{9} undoes the multiplication by \frac{1}{9}.

$$g=\frac{\frac{k}{9}-\frac{h}{9}+f}{\frac{1}{9}}$$

Divide f-\frac{h}{9}+\frac{k}{9} by \frac{1}{9} by multiplying f-\frac{h}{9}+\frac{k}{9} by the reciprocal of \frac{1}{9}.

$$g=9f-h+k$$

Solve for f

$$f=\frac{g+h-k}{9}$$

Solution Steps

Use the distributive property to multiply \frac{1}{9} by g+h-k.

$$f=\frac{1}{9}g+\frac{1}{9}h-\frac{1}{9}k$$