Solve w=-P(V_{2}-V_{1})

$$w = - P ( V _ { 2 } - V _ { 1 } )$$

Solve for P

$$\left\{\begin{matrix}P=\frac{w}{V_{1}-V_{2}}\text{, }&V_{2}\neq V_{1}\\P\in \mathrm{R}\text{, }&w=0\text{ and }V_{2}=V_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -P by V_{2}-V_{1}.

$$w=\left(-P\right)V_{2}-\left(-P\right)V_{1}$$

Multiply -1 and -1 to get 1.

$$w=\left(-P\right)V_{2}+PV_{1}$$

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

$$\left(-P\right)V_{2}+PV_{1}=w$$

Reorder the terms.

$$PV_{1}-PV_{2}=w$$

Combine all terms containing P.

$$\left(V_{1}-V_{2}\right)P=w$$

Divide both sides by -V_{2}+V_{1}.

$$\frac{\left(V_{1}-V_{2}\right)P}{V_{1}-V_{2}}=\frac{w}{V_{1}-V_{2}}$$

Dividing by -V_{2}+V_{1} undoes the multiplication by -V_{2}+V_{1}.

$$P=\frac{w}{V_{1}-V_{2}}$$

Solve for V_1

$$\left\{\begin{matrix}V_{1}=V_{2}+\frac{w}{P}\text{, }&P\neq 0\\V_{1}\in \mathrm{R}\text{, }&w=0\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -P by V_{2}-V_{1}.

$$w=\left(-P\right)V_{2}-\left(-P\right)V_{1}$$

Multiply -1 and -1 to get 1.

$$w=\left(-P\right)V_{2}+PV_{1}$$

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

$$\left(-P\right)V_{2}+PV_{1}=w$$

Subtract \left(-P\right)V_{2} from both sides.

$$PV_{1}=w-\left(-P\right)V_{2}$$

Multiply -1 and -1 to get 1.

$$PV_{1}=w+PV_{2}$$

Divide both sides by P.

$$\frac{PV_{1}}{P}=\frac{w+PV_{2}}{P}$$

Dividing by P undoes the multiplication by P.

$$V_{1}=\frac{w+PV_{2}}{P}$$

Divide V_{2}P+w by P.

$$V_{1}=V_{2}+\frac{w}{P}$$