Solve 30*F/30+r=20_{Omega}

$$\frac { 30 \times F } { 30 + r } = 20 _ { \Omega }$$

Solve for F

$$F=\frac{2\left(r+30\right)}{3}$$

$$r\neq -30$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r+30.

$$30F=20\left(r+30\right)$$

Use the distributive property to multiply 20 by r+30.

$$30F=20r+600$$

Divide both sides by 30.

$$\frac{30F}{30}=\frac{20r+600}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$F=\frac{20r+600}{30}$$

Divide 600+20r by 30.

$$F=\frac{2r}{3}+20$$

Solve for r

$$r=\frac{3\left(F-20\right)}{2}$$

$$F\neq 0$$

Steps for Solving Linear Equation

Variable r cannot be equal to -30 since division by zero is not defined. Multiply both sides of the equation by r+30.

$$30F=20\left(r+30\right)$$

Use the distributive property to multiply 20 by r+30.

$$30F=20r+600$$

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

$$20r+600=30F$$

Subtract 600 from both sides.

$$20r=30F-600$$

Divide both sides by 20.

$$\frac{20r}{20}=\frac{30F-600}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$r=\frac{30F-600}{20}$$

Divide -600+30F by 20.

$$r=\frac{3F}{2}-30$$

Variable r cannot be equal to -30.

$$r=\frac{3F}{2}-30\text{, }r\neq -30$$