Solve Q_{a}=100-10P+0.5m

$$Q _ { a } = 100 - 10 P + 0.5 m$$

Solve for P

$$P=\frac{m-2Q_{a}+200}{20}$$

Steps for Solving Linear Equation

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

$$100-10P+0.5m=Q_{a}$$

Subtract 100 from both sides.

$$-10P+0.5m=Q_{a}-100$$

Subtract 0.5m from both sides.

$$-10P=Q_{a}-100-0.5m$$

The equation is in standard form.

$$-10P=-\frac{m}{2}+Q_{a}-100$$

Divide both sides by -10.

$$\frac{-10P}{-10}=\frac{-\frac{m}{2}+Q_{a}-100}{-10}$$

Dividing by -10 undoes the multiplication by -10.

$$P=\frac{-\frac{m}{2}+Q_{a}-100}{-10}$$

Divide Q_{a}-100-\frac{m}{2} by -10.

$$P=\frac{m}{20}-\frac{Q_{a}}{10}+10$$

Solve for Q_a

$$Q_{a}=\frac{m}{2}-10P+100$$