Solve L_{1}=nA+L_{m}

$$L _ { 1 } = n A + L _ { m }$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{L_{m}-L_{1}}{n}\text{, }&n\neq 0\\A\in \mathrm{R}\text{, }&L_{1}=L_{m}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$nA+L_{m}=L_{1}$$

Subtract L_{m} from both sides.

$$nA=L_{1}-L_{m}$$

Divide both sides by n.

$$\frac{nA}{n}=\frac{L_{1}-L_{m}}{n}$$

Dividing by n undoes the multiplication by n.

$$A=\frac{L_{1}-L_{m}}{n}$$

Solve for L_1

$$L_{1}=An+L_{m}$$