Solve y=1/2+w/3

$$y = \frac { 1 } { 2 } + \frac { w } { 3 }$$

Solve for w

$$w=3y-\frac{3}{2}$$

Steps for Solving Linear Equation

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

$$y=\frac{3}{6}+\frac{2w}{6}$$

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

$$y=\frac{3+2w}{6}$$

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

$$y=\frac{1}{2}+\frac{1}{3}w$$

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

$$\frac{1}{2}+\frac{1}{3}w=y$$

Subtract \frac{1}{2} from both sides.

$$\frac{1}{3}w=y-\frac{1}{2}$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}w}{\frac{1}{3}}=\frac{y-\frac{1}{2}}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$w=\frac{y-\frac{1}{2}}{\frac{1}{3}}$$

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

$$w=3y-\frac{3}{2}$$

Solve for y

$$y=\frac{w}{3}+\frac{1}{2}$$

Solution Steps

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

$$y=\frac{3}{6}+\frac{2w}{6}$$

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

$$y=\frac{3+2w}{6}$$

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

$$y=\frac{1}{2}+\frac{1}{3}w$$