Solve 8pik/4=npi/4+pik

$$\frac { 8 \pi k } { 4 } = \frac { n \pi } { 4 } + \pi k$$

Solve for k

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

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

Subtract 4\pi k from both sides.

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

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

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

Cancel out \pi on both sides.

$$4k=n$$

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

Solve for n

$$n=4k$$

Solution Steps

Multiply both sides of the equation by 4.

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

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

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

Subtract 4\pi k from both sides.

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

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

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

Cancel out \pi on both sides.

$$n=4k$$