Solve R_{n}=R_{1}(1+alphaDeltaB)

$$R _ { n } = R _ { 1 } ( 1 + \alpha \Delta B )$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{R_{1}-R_{n}}{R_{1}\Delta \alpha }\text{, }&R_{1}\neq 0\text{ and }\Delta \neq 0\text{ and }\alpha \neq 0\\B\in \mathrm{R}\text{, }&\left(R_{n}=0\text{ and }R_{1}=0\right)\text{ or }\left(R_{n}=R_{1}\text{ and }\Delta =0\text{ and }R_{1}\neq 0\right)\text{ or }\left(R_{n}=R_{1}\text{ and }\alpha =0\text{ and }\Delta \neq 0\text{ and }R_{1}\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply R_{1} by 1+\alpha \Delta B.

$$R_{n}=R_{1}+R_{1}\alpha \Delta B$$

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

$$R_{1}+R_{1}\alpha \Delta B=R_{n}$$

Subtract R_{1} from both sides.

$$R_{1}\alpha \Delta B=R_{n}-R_{1}$$

The equation is in standard form.

$$R_{1}\Delta \alpha B=R_{n}-R_{1}$$

Divide both sides by R_{1}\alpha \Delta .

$$\frac{R_{1}\Delta \alpha B}{R_{1}\Delta \alpha }=\frac{R_{n}-R_{1}}{R_{1}\Delta \alpha }$$

Dividing by R_{1}\alpha \Delta undoes the multiplication by R_{1}\alpha \Delta .

$$B=\frac{R_{n}-R_{1}}{R_{1}\Delta \alpha }$$

Solve for R_1

$$\left\{\begin{matrix}R_{1}=\frac{R_{n}}{B\Delta \alpha +1}\text{, }&B=0\text{ or }\Delta =0\text{ or }\alpha \neq -\frac{1}{B\Delta }\\R_{1}\in \mathrm{R}\text{, }&R_{n}=0\text{ and }\alpha =-\frac{1}{B\Delta }\text{ and }B\neq 0\text{ and }\Delta \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply R_{1} by 1+\alpha \Delta B.

$$R_{n}=R_{1}+R_{1}\alpha \Delta B$$

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

$$R_{1}+R_{1}\alpha \Delta B=R_{n}$$

Combine all terms containing R_{1}.

$$\left(1+\alpha \Delta B\right)R_{1}=R_{n}$$

The equation is in standard form.

$$\left(B\Delta \alpha +1\right)R_{1}=R_{n}$$

Divide both sides by 1+\alpha \Delta B.

$$\frac{\left(B\Delta \alpha +1\right)R_{1}}{B\Delta \alpha +1}=\frac{R_{n}}{B\Delta \alpha +1}$$

Dividing by 1+\alpha \Delta B undoes the multiplication by 1+\alpha \Delta B.

$$R_{1}=\frac{R_{n}}{B\Delta \alpha +1}$$