Solve (x)=g(x)-2

$$( x ) = g ( x ) - 2$$

Solve for g

$$g=\frac{x+2}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$gx-2=x$$

Add 2 to both sides.

$$gx=x+2$$

The equation is in standard form.

$$xg=x+2$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{x+2}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{x+2}{x}$$

Solve for x

$$x=-\frac{2}{1-g}$$

$$g\neq 1$$

Steps for Solving Linear Equation

Subtract gx from both sides.

$$x-gx=-2$$

Combine all terms containing x.

$$\left(1-g\right)x=-2$$

Divide both sides by 1-g.

$$\frac{\left(1-g\right)x}{1-g}=-\frac{2}{1-g}$$

Dividing by 1-g undoes the multiplication by 1-g.

$$x=-\frac{2}{1-g}$$