Solve 12x-pi/6=pi/2+2kpi

$$\frac{ 12x- \pi }{ 6 } = \frac{ \pi }{ 2 } +2k \pi$$

Solve for k

$$k=\frac{x}{\pi }-\frac{1}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 6,2.

$$12x-\pi =3\pi +12k\pi$$

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

$$3\pi +12k\pi =12x-\pi$$

Subtract 3\pi from both sides.

$$12k\pi =12x-\pi -3\pi$$

Combine -\pi and -3\pi to get -4\pi .

$$12k\pi =12x-4\pi$$

The equation is in standard form.

$$12\pi k=12x-4\pi$$

Divide both sides by 12\pi .

$$\frac{12\pi k}{12\pi }=\frac{12x-4\pi }{12\pi }$$

Dividing by 12\pi undoes the multiplication by 12\pi .

$$k=\frac{12x-4\pi }{12\pi }$$

Divide 12x-4\pi by 12\pi .

$$k=\frac{x}{\pi }-\frac{1}{3}$$

Solve for x

$$x=\pi k+\frac{\pi }{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 6,2.

$$12x-\pi =3\pi +12k\pi$$

Add \pi to both sides.

$$12x=3\pi +12k\pi +\pi$$

Combine 3\pi and \pi to get 4\pi .

$$12x=4\pi +12k\pi$$

The equation is in standard form.

$$12x=12\pi k+4\pi$$

Divide both sides by 12.

$$\frac{12x}{12}=\frac{12\pi k+4\pi }{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x=\frac{12\pi k+4\pi }{12}$$

Divide 4\pi +12\pi k by 12.

$$x=\pi k+\frac{\pi }{3}$$