Solve r:g=1/4x+3

$$r : g = \frac { 1 } { 4 } x + 3$$

Solve for g

$$\left\{\begin{matrix}g=\frac{4r}{x+12}\text{, }&r\neq 0\text{ and }x\neq -12\\g\neq 0\text{, }&x=-12\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4g, the least common multiple of g,4.

$$4r=\frac{1}{4}x\times 4g+4g\times 3$$

Multiply \frac{1}{4} and 4 to get 1.

$$4r=xg+4g\times 3$$

Multiply 4 and 3 to get 12.

$$4r=xg+12g$$

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

$$xg+12g=4r$$

Combine all terms containing g.

$$\left(x+12\right)g=4r$$

Divide both sides by x+12.

$$\frac{\left(x+12\right)g}{x+12}=\frac{4r}{x+12}$$

Dividing by x+12 undoes the multiplication by x+12.

$$g=\frac{4r}{x+12}$$

Variable g cannot be equal to 0.

$$g=\frac{4r}{x+12}\text{, }g\neq 0$$

Solve for r

$$r=\frac{g\left(x+12\right)}{4}$$

$$g\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4g, the least common multiple of g,4.

$$4r=\frac{1}{4}x\times 4g+4g\times 3$$

Multiply \frac{1}{4} and 4 to get 1.

$$4r=xg+4g\times 3$$

Multiply 4 and 3 to get 12.

$$4r=xg+12g$$

The equation is in standard form.

$$4r=gx+12g$$

Divide both sides by 4.

$$\frac{4r}{4}=\frac{g\left(x+12\right)}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$r=\frac{g\left(x+12\right)}{4}$$