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

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

Solve for k

$$k=\frac{x}{\pi }+\frac{3}{8}$$

Steps for Solving Linear Equation

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

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

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

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

Add 2\pi to both sides.

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

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

$$8k\pi =8x+3\pi$$

The equation is in standard form.

$$8\pi k=8x+3\pi$$

Divide both sides by 8\pi .

$$\frac{8\pi k}{8\pi }=\frac{8x+3\pi }{8\pi }$$

Dividing by 8\pi undoes the multiplication by 8\pi .

$$k=\frac{8x+3\pi }{8\pi }$$

Divide 8x+3\pi by 8\pi .

$$k=\frac{x}{\pi }+\frac{3}{8}$$

Solve for x

$$x=\pi k-\frac{3\pi }{8}$$

Steps for Solving Linear Equation

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

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

Subtract \pi from both sides.

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

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

$$8x=-3\pi +8k\pi$$

The equation is in standard form.

$$8x=8\pi k-3\pi$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{\pi \left(8k-3\right)}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{\pi \left(8k-3\right)}{8}$$

Divide \pi \left(-3+8k\right) by 8.

$$x=\pi k-\frac{3\pi }{8}$$