Solve 2pik-npi/4=pi/4+pik

$$2 \pi k - \frac { n \pi } { 4 } = \frac { \pi } { 4 } + \pi k$$

Solve for k

$$k=\frac{n+1}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$8\pi k-n\pi =\pi +4\pi k$$

Subtract 4\pi k from both sides.

$$8\pi k-n\pi -4\pi k=\pi$$

Combine 8\pi k and -4\pi k to get 4\pi k.

$$4\pi k-n\pi =\pi$$

Add n\pi to both sides.

$$4\pi k=\pi +n\pi$$

The equation is in standard form.

$$4\pi k=\pi n+\pi$$

Divide both sides by 4\pi .

$$\frac{4\pi k}{4\pi }=\frac{\pi n+\pi }{4\pi }$$

Dividing by 4\pi undoes the multiplication by 4\pi .

$$k=\frac{\pi n+\pi }{4\pi }$$

Divide \pi +\pi n by 4\pi .

$$k=\frac{n+1}{4}$$

Solve for n

$$n=4k-1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$8\pi k-n\pi =\pi +4\pi k$$

Subtract 8\pi k from both sides.

$$-n\pi =\pi +4\pi k-8\pi k$$

Combine 4\pi k and -8\pi k to get -4\pi k.

$$-n\pi =\pi -4\pi k$$

Reorder the terms.

$$-\pi n=-4\pi k+\pi$$

The equation is in standard form.

$$\left(-\pi \right)n=\pi -4\pi k$$

Divide both sides by -\pi .

$$\frac{\left(-\pi \right)n}{-\pi }=\frac{\pi -4\pi k}{-\pi }$$

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

$$n=\frac{\pi -4\pi k}{-\pi }$$

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

$$n=4k-1$$