Solve 2x=-5pi/6+2kpi

$$2x = - \frac{ 5 \pi }{ 6 } +2k \pi$$

Solve for k

$$k=\frac{x}{\pi }+\frac{5}{12}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$12x=-5\pi +12k\pi$$

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

$$-5\pi +12k\pi =12x$$

Add 5\pi to both sides.

$$12k\pi =12x+5\pi$$

The equation is in standard form.

$$12\pi k=12x+5\pi$$

Divide both sides by 12\pi .

$$\frac{12\pi k}{12\pi }=\frac{12x+5\pi }{12\pi }$$

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

$$k=\frac{12x+5\pi }{12\pi }$$

Divide 12x+5\pi by 12\pi .

$$k=\frac{x}{\pi }+\frac{5}{12}$$

Solve for x

$$x=\pi k-\frac{5\pi }{12}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$12x=-5\pi +12k\pi$$

The equation is in standard form.

$$12x=12\pi k-5\pi$$

Divide both sides by 12.

$$\frac{12x}{12}=\frac{\pi \left(12k-5\right)}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x=\frac{\pi \left(12k-5\right)}{12}$$

Divide \pi \left(-5+12k\right) by 12.

$$x=\pi k-\frac{5\pi }{12}$$