Solve 2x+pi/4=kpi+pi/2

$$2 x + \frac { \pi } { 4 } = k \pi + \frac { \pi } { 2 }$$

Solve for k

$$k=\frac{2x}{\pi }-\frac{1}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$8x+\pi =4k\pi +2\pi$$

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

$$4k\pi +2\pi =8x+\pi$$

Subtract 2\pi from both sides.

$$4k\pi =8x+\pi -2\pi$$

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

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

The equation is in standard form.

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

Divide both sides by 4\pi .

$$\frac{4\pi k}{4\pi }=\frac{8x-\pi }{4\pi }$$

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

$$k=\frac{8x-\pi }{4\pi }$$

Divide 8x-\pi by 4\pi .

$$k=\frac{2x}{\pi }-\frac{1}{4}$$

Solve for x

$$x=\frac{\pi \left(4k+1\right)}{8}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$8x+\pi =4k\pi +2\pi$$

Subtract \pi from both sides.

$$8x=4k\pi +2\pi -\pi$$

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

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

The equation is in standard form.

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

Divide both sides by 8.

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

Dividing by 8 undoes the multiplication by 8.

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

Divide 4\pi k+\pi by 8.

$$x=\frac{\pi k}{2}+\frac{\pi }{8}$$