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

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

Solve for k

$$k=\frac{3x}{4\pi }+\frac{1}{12}$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 3x from both sides.

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

Combine 12x and -3x to get 9x.

$$12k\pi =9x+\pi$$

The equation is in standard form.

$$12\pi k=9x+\pi$$

Divide both sides by 12\pi .

$$\frac{12\pi k}{12\pi }=\frac{9x+\pi }{12\pi }$$

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

$$k=\frac{9x+\pi }{12\pi }$$

Divide 9x+\pi by 12\pi .

$$k=\frac{3x}{4\pi }+\frac{1}{12}$$

Solve for x

$$x=\frac{\pi \left(12k-1\right)}{9}$$

Steps for Solving Linear Equation

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

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

Subtract 3x from both sides.

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

Combine 12x and -3x to get 9x.

$$9x+\pi =12k\pi$$

Subtract \pi from both sides.

$$9x=12k\pi -\pi$$

The equation is in standard form.

$$9x=12\pi k-\pi$$

Divide both sides by 9.

$$\frac{9x}{9}=\frac{\pi \left(12k-1\right)}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x=\frac{\pi \left(12k-1\right)}{9}$$

Divide \pi \left(-1+12k\right) by 9.

$$x=\frac{4\pi k}{3}-\frac{\pi }{9}$$