Solve 2x+varphi=kpi+pi/2

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

Solve for k

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

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

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

Subtract \pi from both sides.

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

The equation is in standard form.

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

Divide both sides by 2\pi .

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

Dividing by 2\pi undoes the multiplication by 2\pi .

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

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

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

Solve for x

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Subtract 2\phi from both sides.

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

The equation is in standard form.

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

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

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

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