Solve x=1/3x+1/2(1/3x)+1/2(frac{1}{2}*frac{1}{3}x)

$$x = \frac { 1 } { 3 } x + \frac { 1 } { 2 } ( \frac { 1 } { 3 } x ) + \frac { 1 } { 2 } ( \frac { 1 } { 2 } \cdot \frac { 1 } { 3 } x )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

$$x=\frac{1}{3}x+\frac{1}{6}x+\frac{1}{2}\times \frac{1}{2}\times \frac{1}{3}x$$

Combine \frac{1}{3}x and \frac{1}{6}x to get \frac{1}{2}x.

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

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$x=\frac{1}{2}x+\frac{1}{4}\times \frac{1}{3}x$$

Multiply \frac{1}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1}{2}x+\frac{1\times 1}{4\times 3}x$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 3}.

$$x=\frac{1}{2}x+\frac{1}{12}x$$

Combine \frac{1}{2}x and \frac{1}{12}x to get \frac{7}{12}x.

$$x=\frac{7}{12}x$$

Subtract \frac{7}{12}x from both sides.

$$x-\frac{7}{12}x=0$$

Combine x and -\frac{7}{12}x to get \frac{5}{12}x.

$$\frac{5}{12}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since \frac{5}{12} is not equal to 0, x must be equal to 0.

$$x=0$$