Solve pi/5-x=pi/3+2kpi

$$\frac { \pi } { 5 } - x = \frac { \pi } { 3 } + 2 k \pi$$

Solve for k

$$k=-\frac{x}{2\pi }-\frac{1}{15}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\pi -15x=5\pi +30k\pi$$

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

$$5\pi +30k\pi =3\pi -15x$$

Subtract 5\pi from both sides.

$$30k\pi =3\pi -15x-5\pi$$

Combine 3\pi and -5\pi to get -2\pi .

$$30k\pi =-2\pi -15x$$

The equation is in standard form.

$$30\pi k=-15x-2\pi$$

Divide both sides by 30\pi .

$$\frac{30\pi k}{30\pi }=\frac{-15x-2\pi }{30\pi }$$

Dividing by 30\pi undoes the multiplication by 30\pi .

$$k=\frac{-15x-2\pi }{30\pi }$$

Divide -2\pi -15x by 30\pi .

$$k=-\frac{x}{2\pi }-\frac{1}{15}$$

Solve for x

$$x=\frac{2\pi \left(-15k-1\right)}{15}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\pi -15x=5\pi +30k\pi$$

Subtract 3\pi from both sides.

$$-15x=5\pi +30k\pi -3\pi$$

Combine 5\pi and -3\pi to get 2\pi .

$$-15x=2\pi +30k\pi$$

The equation is in standard form.

$$-15x=30\pi k+2\pi$$

Divide both sides by -15.

$$\frac{-15x}{-15}=\frac{30\pi k+2\pi }{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$x=\frac{30\pi k+2\pi }{-15}$$

Divide 2\pi +30\pi k by -15.

$$x=-2\pi k-\frac{2\pi }{15}$$