Solve 28cm+42cm=1/2m+Icm

$$28cm+42cm = \frac{ 1 }{ 2 } m+Icm$$

Solve for I

$$\left\{\begin{matrix}I=70-\frac{1}{2c}\text{, }&c\neq 0\\I\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 28cm and 42cm to get 70cm.

$$70cm=\frac{1}{2}m+Icm$$

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

$$\frac{1}{2}m+Icm=70cm$$

Subtract \frac{1}{2}m from both sides.

$$Icm=70cm-\frac{1}{2}m$$

The equation is in standard form.

$$cmI=70cm-\frac{m}{2}$$

Divide both sides by cm.

$$\frac{cmI}{cm}=\frac{70cm-\frac{m}{2}}{cm}$$

Dividing by cm undoes the multiplication by cm.

$$I=\frac{70cm-\frac{m}{2}}{cm}$$

Divide -\frac{m}{2}+70mc by cm.

$$I=70-\frac{1}{2c}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{1}{2\left(70-I\right)}\text{, }&I\neq 70\\c\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 28cm and 42cm to get 70cm.

$$70cm=\frac{1}{2}m+Icm$$

Subtract Icm from both sides.

$$70cm-Icm=\frac{1}{2}m$$

Reorder the terms.

$$-Icm+70cm=\frac{1}{2}m$$

Combine all terms containing c.

$$\left(-Im+70m\right)c=\frac{1}{2}m$$

The equation is in standard form.

$$\left(70m-Im\right)c=\frac{m}{2}$$

Divide both sides by -Im+70m.

$$\frac{\left(70m-Im\right)c}{70m-Im}=\frac{m}{2\left(70m-Im\right)}$$

Dividing by -Im+70m undoes the multiplication by -Im+70m.

$$c=\frac{m}{2\left(70m-Im\right)}$$

Divide \frac{m}{2} by -Im+70m.

$$c=\frac{1}{2\left(70-I\right)}$$