Solve (1/3+11p)=v/z(z)

$$( \frac { 1 } { 3 } + 11 p ) = \frac { v } { z } ( z )$$

Solve for p

$$p=\frac{v}{11}-\frac{1}{33}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3z, the least common multiple of 3,z.

$$3z\times \frac{1}{3}+11p\times 3z=3vz$$

Multiply 3 and \frac{1}{3} to get 1.

$$z+11p\times 3z=3vz$$

Multiply 11 and 3 to get 33.

$$z+33pz=3vz$$

Subtract z from both sides.

$$33pz=3vz-z$$

The equation is in standard form.

$$33zp=3vz-z$$

Divide both sides by 33z.

$$\frac{33zp}{33z}=\frac{z\left(3v-1\right)}{33z}$$

Dividing by 33z undoes the multiplication by 33z.

$$p=\frac{z\left(3v-1\right)}{33z}$$

Divide z\left(-1+3v\right) by 33z.

$$p=\frac{v}{11}-\frac{1}{33}$$

Solve for v

$$v=11p+\frac{1}{3}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3z, the least common multiple of 3,z.

$$3z\times \frac{1}{3}+11p\times 3z=3vz$$

Multiply 3 and \frac{1}{3} to get 1.

$$z+11p\times 3z=3vz$$

Multiply 11 and 3 to get 33.

$$z+33pz=3vz$$

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

$$3vz=z+33pz$$

The equation is in standard form.

$$3zv=33pz+z$$

Divide both sides by 3z.

$$\frac{3zv}{3z}=\frac{33pz+z}{3z}$$

Dividing by 3z undoes the multiplication by 3z.

$$v=\frac{33pz+z}{3z}$$

Divide z+33zp by 3z.

$$v=11p+\frac{1}{3}$$