Solve y=x/2-2/3

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

Solve for x

$$x=2y+\frac{4}{3}$$

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{x}{2} times \frac{3}{3}. Multiply \frac{2}{3} times \frac{2}{2}.

$$y=\frac{3x}{6}-\frac{2\times 2}{6}$$

Since \frac{3x}{6} and \frac{2\times 2}{6} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{3x-2\times 2}{6}$$

Do the multiplications in 3x-2\times 2.

$$y=\frac{3x-4}{6}$$

Divide each term of 3x-4 by 6 to get \frac{1}{2}x-\frac{2}{3}.

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

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

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

Add \frac{2}{3} to both sides.

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

Multiply both sides by 2.

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

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

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

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

$$x=2y+\frac{4}{3}$$

Solve for y

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

Short 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{x}{2} times \frac{3}{3}. Multiply \frac{2}{3} times \frac{2}{2}.

$$y=\frac{3x}{6}-\frac{2\times 2}{6}$$

Since \frac{3x}{6} and \frac{2\times 2}{6} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{3x-2\times 2}{6}$$

Do the multiplications in 3x-2\times 2.

$$y=\frac{3x-4}{6}$$

Divide each term of 3x-4 by 6 to get \frac{1}{2}x-\frac{2}{3}.

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