Solve r=2L-20/2L+20

$$r = \frac { 2 L - 20 } { 2 L + 20 }$$

Solve for L

$$L=-\frac{10\left(r+1\right)}{r-1}$$

$$r\neq 1$$

Steps for Solving Linear Equation

Variable L cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by 2\left(L+10\right).

$$r\times 2\left(L+10\right)=2L-20$$

Use the distributive property to multiply r\times 2 by L+10.

$$2rL+10r\times 2=2L-20$$

Multiply 10 and 2 to get 20.

$$2rL+20r=2L-20$$

Subtract 2L from both sides.

$$2rL+20r-2L=-20$$

Subtract 20r from both sides.

$$2rL-2L=-20-20r$$

Combine all terms containing L.

$$\left(2r-2\right)L=-20-20r$$

The equation is in standard form.

$$\left(2r-2\right)L=-20r-20$$

Divide both sides by 2r-2.

$$\frac{\left(2r-2\right)L}{2r-2}=\frac{-20r-20}{2r-2}$$

Dividing by 2r-2 undoes the multiplication by 2r-2.

$$L=\frac{-20r-20}{2r-2}$$

Divide -20-20r by 2r-2.

$$L=-\frac{10\left(r+1\right)}{r-1}$$

Variable L cannot be equal to -10.

$$L=-\frac{10\left(r+1\right)}{r-1}\text{, }L\neq -10$$

Solve for r

$$r=-\frac{10-L}{L+10}$$

$$L\neq -10$$