Solve E=frac{C_{e}-C_{s}}{C_{e}}*100

$$E = \frac { C _ { e } - C _ { s } } { C _ { e } } \cdot 100$$

Solve for C_e

$$\left\{\begin{matrix}C_{e}=\frac{100C_{s}}{100-E}\text{, }&C_{s}\neq 0\text{ and }E\neq 100\\C_{e}\neq 0\text{, }&C_{s}=0\text{ and }E=100\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable C_{e} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by C_{e}.

$$EC_{e}=\left(C_{e}-C_{s}\right)\times 100$$

Use the distributive property to multiply C_{e}-C_{s} by 100.

$$EC_{e}=100C_{e}-100C_{s}$$

Subtract 100C_{e} from both sides.

$$EC_{e}-100C_{e}=-100C_{s}$$

Combine all terms containing C_{e}.

$$\left(E-100\right)C_{e}=-100C_{s}$$

Divide both sides by E-100.

$$\frac{\left(E-100\right)C_{e}}{E-100}=-\frac{100C_{s}}{E-100}$$

Dividing by E-100 undoes the multiplication by E-100.

$$C_{e}=-\frac{100C_{s}}{E-100}$$

Variable C_{e} cannot be equal to 0.

$$C_{e}=-\frac{100C_{s}}{E-100}\text{, }C_{e}\neq 0$$

Solve for C_s

$$C_{s}=-\frac{C_{e}E}{100}+C_{e}$$

$$C_{e}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by C_{e}.

$$EC_{e}=\left(C_{e}-C_{s}\right)\times 100$$

Use the distributive property to multiply C_{e}-C_{s} by 100.

$$EC_{e}=100C_{e}-100C_{s}$$

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

$$100C_{e}-100C_{s}=EC_{e}$$

Subtract 100C_{e} from both sides.

$$-100C_{s}=EC_{e}-100C_{e}$$

The equation is in standard form.

$$-100C_{s}=C_{e}E-100C_{e}$$

Divide both sides by -100.

$$\frac{-100C_{s}}{-100}=\frac{C_{e}\left(E-100\right)}{-100}$$

Dividing by -100 undoes the multiplication by -100.

$$C_{s}=\frac{C_{e}\left(E-100\right)}{-100}$$

Divide C_{e}\left(-100+E\right) by -100.

$$C_{s}=-\frac{C_{e}E}{100}+C_{e}$$