Solve sqrt{2}mmux-x+3=0

$$\sqrt { 2 } m \mu x - x + 3 = 0$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{\sqrt{2}\left(3-x\right)}{2x\mu }\text{, }&x\neq 0\text{ and }\mu \neq 0\\m\in \mathrm{R}\text{, }&x=3\text{ and }\mu =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides. Anything plus zero gives itself.

$$\sqrt{2}m\mu x+3=x$$

Subtract 3 from both sides.

$$\sqrt{2}m\mu x=x-3$$

The equation is in standard form.

$$\sqrt{2}x\mu m=x-3$$

Divide both sides by \sqrt{2}\mu x.

$$\frac{\sqrt{2}x\mu m}{\sqrt{2}x\mu }=\frac{x-3}{\sqrt{2}x\mu }$$

Dividing by \sqrt{2}\mu x undoes the multiplication by \sqrt{2}\mu x.

$$m=\frac{x-3}{\sqrt{2}x\mu }$$

Divide x-3 by \sqrt{2}\mu x.

$$m=\frac{\sqrt{2}\left(x-3\right)}{2x\mu }$$

Solve for x

$$x=-\frac{3}{\sqrt{2}m\mu -1}$$

$$\mu =0\text{ or }m\neq \frac{\sqrt{2}}{2\mu }$$

Steps for Solving Linear Equation

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{2}m\mu x-x=-3$$

Combine all terms containing x.

$$\left(\sqrt{2}m\mu -1\right)x=-3$$

Divide both sides by \sqrt{2}m\mu -1.

$$\frac{\left(\sqrt{2}m\mu -1\right)x}{\sqrt{2}m\mu -1}=-\frac{3}{\sqrt{2}m\mu -1}$$

Dividing by \sqrt{2}m\mu -1 undoes the multiplication by \sqrt{2}m\mu -1.

$$x=-\frac{3}{\sqrt{2}m\mu -1}$$