Solve 2x+1=pi/2+k*2pi

$$2 x + 1 = \frac { \pi } { 2 } + k \cdot 2 \pi$$

Solve for k

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Multiply 2 and 2 to get 4.

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

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

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

Subtract \pi from both sides.

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

The equation is in standard form.

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

Divide both sides by 4\pi .

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

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

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

Divide 4x+2-\pi by 4\pi .

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

Solve for x

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Multiply 2 and 2 to get 4.

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

Subtract 2 from both sides.

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

The equation is in standard form.

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

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

Divide \pi +4k\pi -2 by 4.

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