Solve dW_{3}-dW_{4}+dI_{4}=0

$$d W _ { 3 } - d W _ { 4 } + d I _ { 4 } = 0$$

Solve for I_4

$$\left\{\begin{matrix}\\I_{4}=W_{4}-W_{3}\text{, }&\text{unconditionally}\\I_{4}\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract dW_{3} from both sides. Anything subtracted from zero gives its negation.

$$-dW_{4}+dI_{4}=-dW_{3}$$

Add dW_{4} to both sides.

$$dI_{4}=-dW_{3}+dW_{4}$$

Reorder the terms.

$$I_{4}d=-W_{3}d+W_{4}d$$

The equation is in standard form.

$$dI_{4}=W_{4}d-W_{3}d$$

Divide both sides by d.

$$\frac{dI_{4}}{d}=\frac{d\left(W_{4}-W_{3}\right)}{d}$$

Dividing by d undoes the multiplication by d.

$$I_{4}=\frac{d\left(W_{4}-W_{3}\right)}{d}$$

Divide d\left(-W_{3}+W_{4}\right) by d.

$$I_{4}=W_{4}-W_{3}$$

Solve for W_3

$$\left\{\begin{matrix}\\W_{3}=W_{4}-I_{4}\text{, }&\text{unconditionally}\\W_{3}\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add dW_{4} to both sides. Anything plus zero gives itself.

$$dW_{3}+dI_{4}=dW_{4}$$

Subtract dI_{4} from both sides.

$$dW_{3}=dW_{4}-dI_{4}$$

The equation is in standard form.

$$dW_{3}=W_{4}d-I_{4}d$$

Divide both sides by d.

$$\frac{dW_{3}}{d}=\frac{d\left(W_{4}-I_{4}\right)}{d}$$

Dividing by d undoes the multiplication by d.

$$W_{3}=\frac{d\left(W_{4}-I_{4}\right)}{d}$$

Divide d\left(W_{4}-I_{4}\right) by d.

$$W_{3}=W_{4}-I_{4}$$