Solve p=1/3+q/2

$$p = \frac { 1 } { 3 } + \frac { q } { 2 }$$

Solve for p

$$p=\frac{q}{2}+\frac{1}{3}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{1}{3} times \frac{2}{2}. Multiply \frac{q}{2} times \frac{3}{3}.

$$p=\frac{2}{6}+\frac{3q}{6}$$

Since \frac{2}{6} and \frac{3q}{6} have the same denominator, add them by adding their numerators.

$$p=\frac{2+3q}{6}$$

Divide each term of 2+3q by 6 to get \frac{1}{3}+\frac{1}{2}q.

$$p=\frac{1}{3}+\frac{1}{2}q$$

Solve for q

$$q=2p-\frac{2}{3}$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{1}{3} times \frac{2}{2}. Multiply \frac{q}{2} times \frac{3}{3}.

$$p=\frac{2}{6}+\frac{3q}{6}$$

Since \frac{2}{6} and \frac{3q}{6} have the same denominator, add them by adding their numerators.

$$p=\frac{2+3q}{6}$$

Divide each term of 2+3q by 6 to get \frac{1}{3}+\frac{1}{2}q.

$$p=\frac{1}{3}+\frac{1}{2}q$$

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

$$\frac{1}{3}+\frac{1}{2}q=p$$

Subtract \frac{1}{3} from both sides.

$$\frac{1}{2}q=p-\frac{1}{3}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}q}{\frac{1}{2}}=\frac{p-\frac{1}{3}}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$q=\frac{p-\frac{1}{3}}{\frac{1}{2}}$$

Divide p-\frac{1}{3} by \frac{1}{2} by multiplying p-\frac{1}{3} by the reciprocal of \frac{1}{2}.

$$q=2p-\frac{2}{3}$$