Solve F^-1(x)=x+7/6

$$F ^ { - 1 } ( x ) = \frac { x + 7 } { 6 }$$

Solve for F

$$F=\frac{6x}{x+7}$$

$$x\neq 0\text{ and }x\neq -7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$6F^{-1}x=x+7$$

Reorder the terms.

$$6\times \frac{1}{F}x=x+7$$

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

$$6\times 1x=Fx+F\times 7$$

Multiply 6 and 1 to get 6.

$$6x=Fx+F\times 7$$

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

$$Fx+F\times 7=6x$$

Combine all terms containing F.

$$\left(x+7\right)F=6x$$

Divide both sides by x+7.

$$\frac{\left(x+7\right)F}{x+7}=\frac{6x}{x+7}$$

Dividing by x+7 undoes the multiplication by x+7.

$$F=\frac{6x}{x+7}$$

Variable F cannot be equal to 0.

$$F=\frac{6x}{x+7}\text{, }F\neq 0$$

Solve for x

$$x=\frac{7F}{6-F}$$

$$F\neq 6\text{ and }F\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$6F^{-1}x=x+7$$

Subtract x from both sides.

$$6F^{-1}x-x=7$$

Reorder the terms.

$$-x+6\times \frac{1}{F}x=7$$

Multiply both sides of the equation by F.

$$-xF+6\times 1x=7F$$

Multiply 6 and 1 to get 6.

$$-xF+6x=7F$$

Combine all terms containing x.

$$\left(-F+6\right)x=7F$$

The equation is in standard form.

$$\left(6-F\right)x=7F$$

Divide both sides by 6-F.

$$\frac{\left(6-F\right)x}{6-F}=\frac{7F}{6-F}$$

Dividing by 6-F undoes the multiplication by 6-F.

$$x=\frac{7F}{6-F}$$