Solve 3(wx-v)=5(x+v)

$$3 ( w x - v ) = 5 ( x + v )$$

Solve for w (complex solution)

$$\left\{\begin{matrix}w=\frac{8v}{3x}+\frac{5}{3}\text{, }&x\neq 0\\w\in \mathrm{C}\text{, }&x=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by wx-v.

$$3wx-3v=5\left(x+v\right)$$

Use the distributive property to multiply 5 by x+v.

$$3wx-3v=5x+5v$$

Add 3v to both sides.

$$3wx=5x+5v+3v$$

Combine 5v and 3v to get 8v.

$$3wx=5x+8v$$

The equation is in standard form.

$$3xw=5x+8v$$

Divide both sides by 3x.

$$\frac{3xw}{3x}=\frac{5x+8v}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$w=\frac{5x+8v}{3x}$$

Divide 5x+8v by 3x.

$$w=\frac{8v}{3x}+\frac{5}{3}$$

Solve for v

$$v=\frac{x\left(3w-5\right)}{8}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by wx-v.

$$3wx-3v=5\left(x+v\right)$$

Use the distributive property to multiply 5 by x+v.

$$3wx-3v=5x+5v$$

Subtract 5v from both sides.

$$3wx-3v-5v=5x$$

Combine -3v and -5v to get -8v.

$$3wx-8v=5x$$

Subtract 3wx from both sides.

$$-8v=5x-3wx$$

Divide both sides by -8.

$$\frac{-8v}{-8}=\frac{x\left(5-3w\right)}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$v=\frac{x\left(5-3w\right)}{-8}$$

Divide x\left(5-3w\right) by -8.

$$v=-\frac{x\left(5-3w\right)}{8}$$

Solve for w

$$\left\{\begin{matrix}w=\frac{8v}{3x}+\frac{5}{3}\text{, }&x\neq 0\\w\in \mathrm{R}\text{, }&x=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by wx-v.

$$3wx-3v=5\left(x+v\right)$$

Use the distributive property to multiply 5 by x+v.

$$3wx-3v=5x+5v$$

Add 3v to both sides.

$$3wx=5x+5v+3v$$

Combine 5v and 3v to get 8v.

$$3wx=5x+8v$$

The equation is in standard form.

$$3xw=5x+8v$$

Divide both sides by 3x.

$$\frac{3xw}{3x}=\frac{5x+8v}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$w=\frac{5x+8v}{3x}$$

Divide 5x+8v by 3x.

$$w=\frac{8v}{3x}+\frac{5}{3}$$