Solve 40ms/mc=100mg/x

$$\frac { 40 m s } { m c } = \frac { 100 m g } { x }$$

Solve for c

$$\left\{\begin{matrix}c=\frac{2sx}{5gm}\text{, }&x\neq 0\text{ and }s\neq 0\text{ and }m\neq 0\text{ and }g\neq 0\\c\neq 0\text{, }&g=0\text{ and }s=0\text{ and }x\neq 0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x\times 40ms=cm\times 100mg$$

Multiply m and m to get m^{2}.

$$x\times 40ms=cm^{2}\times 100g$$

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

$$cm^{2}\times 100g=x\times 40ms$$

The equation is in standard form.

$$100gm^{2}c=40msx$$

Divide both sides by 100m^{2}g.

$$\frac{100gm^{2}c}{100gm^{2}}=\frac{40msx}{100gm^{2}}$$

Dividing by 100m^{2}g undoes the multiplication by 100m^{2}g.

$$c=\frac{40msx}{100gm^{2}}$$

Divide 40xms by 100m^{2}g.

$$c=\frac{2sx}{5gm}$$

Variable c cannot be equal to 0.

$$c=\frac{2sx}{5gm}\text{, }c\neq 0$$

Solve for g

$$g=\frac{2sx}{5cm}$$

$$m\neq 0\text{ and }c\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by cmx, the least common multiple of mc,x.

$$x\times 40ms=cm\times 100mg$$

Multiply m and m to get m^{2}.

$$x\times 40ms=cm^{2}\times 100g$$

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

$$cm^{2}\times 100g=x\times 40ms$$

The equation is in standard form.

$$100cm^{2}g=40msx$$

Divide both sides by 100cm^{2}.

$$\frac{100cm^{2}g}{100cm^{2}}=\frac{40msx}{100cm^{2}}$$

Dividing by 100cm^{2} undoes the multiplication by 100cm^{2}.

$$g=\frac{40msx}{100cm^{2}}$$

Divide 40xms by 100cm^{2}.

$$g=\frac{2sx}{5cm}$$