Solve (3-x)+operatorname{Bg}(x-1)=pi

$$( 3 - x ) + \operatorname { Bg } ( x - 1 ) = \pi$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\frac{-x+3-\pi }{g\left(x-1\right)}\text{, }&x\neq 1\text{ and }g\neq 0\\B\in \mathrm{C}\text{, }&x=3-\pi \text{ and }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply Bg by x-1.

$$3-x+Bgx-Bg=\pi$$

Subtract 3 from both sides.

$$-x+Bgx-Bg=\pi -3$$

Add x to both sides.

$$Bgx-Bg=\pi -3+x$$

Combine all terms containing B.

$$\left(gx-g\right)B=\pi -3+x$$

The equation is in standard form.

$$\left(gx-g\right)B=x+\pi -3$$

Divide both sides by gx-g.

$$\frac{\left(gx-g\right)B}{gx-g}=\frac{x+\pi -3}{gx-g}$$

Dividing by gx-g undoes the multiplication by gx-g.

$$B=\frac{x+\pi -3}{gx-g}$$

Divide x-3+\pi by gx-g.

$$B=\frac{x+\pi -3}{g\left(x-1\right)}$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{-x+3-\pi }{B\left(x-1\right)}\text{, }&x\neq 1\text{ and }B\neq 0\\g\in \mathrm{C}\text{, }&x=3-\pi \text{ and }B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply Bg by x-1.

$$3-x+Bgx-Bg=\pi$$

Subtract 3 from both sides.

$$-x+Bgx-Bg=\pi -3$$

Add x to both sides.

$$Bgx-Bg=\pi -3+x$$

Combine all terms containing g.

$$\left(Bx-B\right)g=\pi -3+x$$

The equation is in standard form.

$$\left(Bx-B\right)g=x+\pi -3$$

Divide both sides by Bx-B.

$$\frac{\left(Bx-B\right)g}{Bx-B}=\frac{x+\pi -3}{Bx-B}$$

Dividing by Bx-B undoes the multiplication by Bx-B.

$$g=\frac{x+\pi -3}{Bx-B}$$

Divide x-3+\pi by Bx-B.

$$g=\frac{x+\pi -3}{B\left(x-1\right)}$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{-x+3-\pi }{g\left(x-1\right)}\text{, }&x\neq 1\text{ and }g\neq 0\\B\in \mathrm{R}\text{, }&x=3-\pi \text{ and }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply Bg by x-1.

$$3-x+Bgx-Bg=\pi$$

Subtract 3 from both sides.

$$-x+Bgx-Bg=\pi -3$$

Add x to both sides.

$$Bgx-Bg=\pi -3+x$$

Combine all terms containing B.

$$\left(gx-g\right)B=\pi -3+x$$

The equation is in standard form.

$$\left(gx-g\right)B=x+\pi -3$$

Divide both sides by gx-g.

$$\frac{\left(gx-g\right)B}{gx-g}=\frac{x+\pi -3}{gx-g}$$

Dividing by gx-g undoes the multiplication by gx-g.

$$B=\frac{x+\pi -3}{gx-g}$$

Divide x-3+\pi by gx-g.

$$B=\frac{x+\pi -3}{g\left(x-1\right)}$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{-x+3-\pi }{B\left(x-1\right)}\text{, }&x\neq 1\text{ and }B\neq 0\\g\in \mathrm{R}\text{, }&x=3-\pi \text{ and }B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply Bg by x-1.

$$3-x+Bgx-Bg=\pi$$

Subtract 3 from both sides.

$$-x+Bgx-Bg=\pi -3$$

Add x to both sides.

$$Bgx-Bg=\pi -3+x$$

Combine all terms containing g.

$$\left(Bx-B\right)g=\pi -3+x$$

The equation is in standard form.

$$\left(Bx-B\right)g=x+\pi -3$$

Divide both sides by Bx-B.

$$\frac{\left(Bx-B\right)g}{Bx-B}=\frac{x+\pi -3}{Bx-B}$$

Dividing by Bx-B undoes the multiplication by Bx-B.

$$g=\frac{x+\pi -3}{Bx-B}$$

Divide x-3+\pi by Bx-B.

$$g=\frac{x+\pi -3}{B\left(x-1\right)}$$