Solve F(x+1)-2=x+7

$$F ( x + 1 ) - 2 = x + 7$$

Solve for F

$$F=\frac{x+9}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply F by x+1.

$$Fx+F-2=x+7$$

Add 2 to both sides.

$$Fx+F=x+7+2$$

Add 7 and 2 to get 9.

$$Fx+F=x+9$$

Combine all terms containing F.

$$\left(x+1\right)F=x+9$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)F}{x+1}=\frac{x+9}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$F=\frac{x+9}{x+1}$$

Solve for x

$$x=-\frac{F-9}{F-1}$$

$$F\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply F by x+1.

$$Fx+F-2=x+7$$

Subtract x from both sides.

$$Fx+F-2-x=7$$

Subtract F from both sides.

$$Fx-2-x=7-F$$

Add 2 to both sides.

$$Fx-x=7-F+2$$

Add 7 and 2 to get 9.

$$Fx-x=9-F$$

Combine all terms containing x.

$$\left(F-1\right)x=9-F$$

Divide both sides by F-1.

$$\frac{\left(F-1\right)x}{F-1}=\frac{9-F}{F-1}$$

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

$$x=\frac{9-F}{F-1}$$