Solve P=(frac{Q_{5}-20}{75})+0.4

$$P = ( \frac { Q _ { 5 } - 20 } { 75 } ) + 0.4$$

Solve for P

$$P=\frac{Q_{5}+10}{75}$$

Solution Steps

Divide each term of Q_{5}-20 by 75 to get \frac{1}{75}Q_{5}-\frac{4}{15}.

$$P=\frac{1}{75}Q_{5}-\frac{4}{15}+0.4$$

Add -\frac{4}{15} and 0.4 to get \frac{2}{15}.

$$P=\frac{1}{75}Q_{5}+\frac{2}{15}$$

Solve for Q_5

$$Q_{5}=75P-10$$

Steps for Solving Linear Equation

Divide each term of Q_{5}-20 by 75 to get \frac{1}{75}Q_{5}-\frac{4}{15}.

$$P=\frac{1}{75}Q_{5}-\frac{4}{15}+0.4$$

Add -\frac{4}{15} and 0.4 to get \frac{2}{15}.

$$P=\frac{1}{75}Q_{5}+\frac{2}{15}$$

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

$$\frac{1}{75}Q_{5}+\frac{2}{15}=P$$

Subtract \frac{2}{15} from both sides.

$$\frac{1}{75}Q_{5}=P-\frac{2}{15}$$

Multiply both sides by 75.

$$\frac{\frac{1}{75}Q_{5}}{\frac{1}{75}}=\frac{P-\frac{2}{15}}{\frac{1}{75}}$$

Dividing by \frac{1}{75} undoes the multiplication by \frac{1}{75}.

$$Q_{5}=\frac{P-\frac{2}{15}}{\frac{1}{75}}$$

Divide P-\frac{2}{15} by \frac{1}{75} by multiplying P-\frac{2}{15} by the reciprocal of \frac{1}{75}.

$$Q_{5}=75P-10$$