Solve g^-1(x)=x-3/7

$$g ^ { - 1 } ( x ) = \frac { x - 3 } { 7 }$$

Solve for g

$$g=-\frac{7x}{3-x}$$

$$x\neq 0\text{ and }x\neq 3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7.

$$7g^{-1}x=x-3$$

Reorder the terms.

$$7\times \frac{1}{g}x=x-3$$

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by g.

$$7\times 1x=gx+g\left(-3\right)$$

Multiply 7 and 1 to get 7.

$$7x=gx+g\left(-3\right)$$

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

$$gx+g\left(-3\right)=7x$$

Combine all terms containing g.

$$\left(x-3\right)g=7x$$

Divide both sides by x-3.

$$\frac{\left(x-3\right)g}{x-3}=\frac{7x}{x-3}$$

Dividing by x-3 undoes the multiplication by x-3.

$$g=\frac{7x}{x-3}$$

Variable g cannot be equal to 0.

$$g=\frac{7x}{x-3}\text{, }g\neq 0$$

Solve for x

$$x=-\frac{3g}{7-g}$$

$$g\neq 7\text{ and }g\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7.

$$7g^{-1}x=x-3$$

Subtract x from both sides.

$$7g^{-1}x-x=-3$$

Reorder the terms.

$$-x+7\times \frac{1}{g}x=-3$$

Multiply both sides of the equation by g.

$$-xg+7\times 1x=-3g$$

Multiply 7 and 1 to get 7.

$$-xg+7x=-3g$$

Combine all terms containing x.

$$\left(-g+7\right)x=-3g$$

The equation is in standard form.

$$\left(7-g\right)x=-3g$$

Divide both sides by 7-g.

$$\frac{\left(7-g\right)x}{7-g}=-\frac{3g}{7-g}$$

Dividing by 7-g undoes the multiplication by 7-g.

$$x=-\frac{3g}{7-g}$$