Solve 2x-pi/6=kpi

$$2 x - \frac { \pi } { 6 } = k \pi$$

Solve for k

$$k=\frac{2x}{\pi }-\frac{1}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$12x-\pi =6k\pi$$

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

$$6k\pi =12x-\pi$$

The equation is in standard form.

$$6\pi k=12x-\pi$$

Divide both sides by 6\pi .

$$\frac{6\pi k}{6\pi }=\frac{12x-\pi }{6\pi }$$

Dividing by 6\pi undoes the multiplication by 6\pi .

$$k=\frac{12x-\pi }{6\pi }$$

Divide 12x-\pi by 6\pi .

$$k=\frac{2x}{\pi }-\frac{1}{6}$$

Solve for x

$$x=\frac{\pi \left(6k+1\right)}{12}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$12x-\pi =6k\pi$$

Add \pi to both sides.

$$12x=6k\pi +\pi$$

The equation is in standard form.

$$12x=6\pi k+\pi$$

Divide both sides by 12.

$$\frac{12x}{12}=\frac{6\pi k+\pi }{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x=\frac{6\pi k+\pi }{12}$$

Divide 6\pi k+\pi by 12.

$$x=\frac{\pi k}{2}+\frac{\pi }{12}$$