Solve 1/2*1+y/2+1/3y=2

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

Solve for y

$$y=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$\frac{3}{2}\left(1+y\right)+2y=12$$

Use the distributive property to multiply \frac{3}{2} by 1+y.

$$\frac{3}{2}+\frac{3}{2}y+2y=12$$

Combine \frac{3}{2}y and 2y to get \frac{7}{2}y.

$$\frac{3}{2}+\frac{7}{2}y=12$$

Subtract \frac{3}{2} from both sides.

$$\frac{7}{2}y=12-\frac{3}{2}$$

Convert 12 to fraction \frac{24}{2}.

$$\frac{7}{2}y=\frac{24}{2}-\frac{3}{2}$$

Since \frac{24}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}y=\frac{24-3}{2}$$

Subtract 3 from 24 to get 21.

$$\frac{7}{2}y=\frac{21}{2}$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.

$$y=\frac{21}{2}\times \frac{2}{7}$$

Multiply \frac{21}{2} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{21\times 2}{2\times 7}$$

Cancel out 2 in both numerator and denominator.

$$y=\frac{21}{7}$$

Divide 21 by 7 to get 3.

$$y=3$$