Solve 3pi/4+kpi=x-3/2pi

$$\frac { 3 \pi } { 4 } + k \pi = x - \frac { 3 } { 2 } \pi$$

Solve for k

$$k=\frac{x}{\pi }-\frac{9}{4}$$

Steps for Solving Linear Equation

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

$$3\pi +4k\pi =4x-6\pi$$

Subtract 3\pi from both sides.

$$4k\pi =4x-6\pi -3\pi$$

Combine -6\pi and -3\pi to get -9\pi .

$$4k\pi =4x-9\pi$$

The equation is in standard form.

$$4\pi k=4x-9\pi$$

Divide both sides by 4\pi .

$$\frac{4\pi k}{4\pi }=\frac{4x-9\pi }{4\pi }$$

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

$$k=\frac{4x-9\pi }{4\pi }$$

Divide 4x-9\pi by 4\pi .

$$k=\frac{x}{\pi }-\frac{9}{4}$$

Solve for x

$$x=\pi k+\frac{9\pi }{4}$$

Steps for Solving Linear Equation

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

$$3\pi +4k\pi =4x-6\pi$$

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

$$4x-6\pi =3\pi +4k\pi$$

Add 6\pi to both sides.

$$4x=3\pi +4k\pi +6\pi$$

Combine 3\pi and 6\pi to get 9\pi .

$$4x=9\pi +4k\pi$$

The equation is in standard form.

$$4x=4\pi k+9\pi$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{\pi \left(4k+9\right)}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{\pi \left(4k+9\right)}{4}$$

Divide \pi \left(9+4k\right) by 4.

$$x=\pi k+\frac{9\pi }{4}$$