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

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

Solve for f

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

Solution Steps

Use the distributive property to multiply \frac{1}{5} by g+h-k.

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

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

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

Solve for g

$$g=5f-h+k$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by g+h-k.

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

Subtract \frac{1}{5}h from both sides.

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

Add \frac{1}{5}k to both sides.

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

The equation is in standard form.

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

Multiply both sides by 5.

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

Dividing by \frac{1}{5} undoes the multiplication by \frac{1}{5}.

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

Divide f-\frac{h}{5}+\frac{k}{5} by \frac{1}{5} by multiplying f-\frac{h}{5}+\frac{k}{5} by the reciprocal of \frac{1}{5}.

$$g=5f-h+k$$