Solve 2g(x-2)=3.f(x-2)

$$2 g ( x - 2 ) = 3 . f ( x - 2 )$$

Solve for g

$$g=\frac{3}{2\left(x-2\right)}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2g by x-2.

$$2gx-4g=3$$

Combine all terms containing g.

$$\left(2x-4\right)g=3$$

Divide both sides by 2x-4.

$$\frac{\left(2x-4\right)g}{2x-4}=\frac{3}{2x-4}$$

Dividing by 2x-4 undoes the multiplication by 2x-4.

$$g=\frac{3}{2x-4}$$

Divide 3 by 2x-4.

$$g=\frac{3}{2\left(x-2\right)}$$

Solve for x

$$x=2+\frac{3}{2g}$$

$$g\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2g by x-2.

$$2gx-4g=3$$

Add 4g to both sides.

$$2gx=3+4g$$

The equation is in standard form.

$$2gx=4g+3$$

Divide both sides by 2g.

$$\frac{2gx}{2g}=\frac{4g+3}{2g}$$

Dividing by 2g undoes the multiplication by 2g.

$$x=\frac{4g+3}{2g}$$

Divide 3+4g by 2g.

$$x=2+\frac{3}{2g}$$