Solve w_{2}-x(y-t_{x})=(w+1)

$$w _ { 2 } - x ( y - t _ { x } ) = ( w + 1 )$$

Solve for t_x (complex solution)

$$\left\{\begin{matrix}t_{x}=\frac{xy+w-w_{2}+1}{x}\text{, }&x\neq 0\\t_{x}\in \mathrm{C}\text{, }&w_{2}=w+1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-t_{x}.

$$w_{2}-\left(xy-xt_{x}\right)=w+1$$

To find the opposite of xy-xt_{x}, find the opposite of each term.

$$w_{2}-xy+xt_{x}=w+1$$

Subtract w_{2} from both sides.

$$-xy+xt_{x}=w+1-w_{2}$$

Add xy to both sides.

$$xt_{x}=w+1-w_{2}+xy$$

The equation is in standard form.

$$xt_{x}=xy+w-w_{2}+1$$

Divide both sides by x.

$$\frac{xt_{x}}{x}=\frac{xy+w-w_{2}+1}{x}$$

Dividing by x undoes the multiplication by x.

$$t_{x}=\frac{xy+w-w_{2}+1}{x}$$

Solve for t_x

$$\left\{\begin{matrix}t_{x}=\frac{xy+w-w_{2}+1}{x}\text{, }&x\neq 0\\t_{x}\in \mathrm{R}\text{, }&w_{2}=w+1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-t_{x}.

$$w_{2}-\left(xy-xt_{x}\right)=w+1$$

To find the opposite of xy-xt_{x}, find the opposite of each term.

$$w_{2}-xy+xt_{x}=w+1$$

Subtract w_{2} from both sides.

$$-xy+xt_{x}=w+1-w_{2}$$

Add xy to both sides.

$$xt_{x}=w+1-w_{2}+xy$$

The equation is in standard form.

$$xt_{x}=xy+w-w_{2}+1$$

Divide both sides by x.

$$\frac{xt_{x}}{x}=\frac{xy+w-w_{2}+1}{x}$$

Dividing by x undoes the multiplication by x.

$$t_{x}=\frac{xy+w-w_{2}+1}{x}$$

Solve for w

$$w=t_{x}x-xy+w_{2}-1$$