Solve (2/3-1/6+1/3-1/12):x=(frac{3}{2}*2*frac{5}{3}:2):(1:frac{2}{3}+frac{1}{18}:frac{1}{3})

$$( \frac { 2 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 3 } - \frac { 1 } { 12 } ) : x = ( \frac { 3 } { 2 } \cdot 2 \cdot \frac { 5 } { 3 } : 2 ) : ( 1 : \frac { 2 } { 3 } + \frac { 1 } { 18 } : \frac { 1 } { 3 } )$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{2}{3}-\frac{1}{6}+\frac{1}{3}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{4}{6}-\frac{1}{6}+\frac{1}{3}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-1}{6}+\frac{1}{3}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Subtract 1 from 4 to get 3.

$$\frac{3}{6}+\frac{1}{3}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}+\frac{1}{3}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{2}{6}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

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

$$\frac{3+2}{6}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Add 3 and 2 to get 5.

$$\frac{5}{6}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Least common multiple of 6 and 12 is 12. Convert \frac{5}{6} and \frac{1}{12} to fractions with denominator 12.

$$\frac{10}{12}-\frac{1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Since \frac{10}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-1}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Subtract 1 from 10 to get 9.

$$\frac{9}{12}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}=\frac{3}{5}x\times \frac{\frac{3}{2}\times 2\times \frac{5}{3}}{2}$$

Cancel out 2 and 2.

$$\frac{3}{4}=\frac{3}{5}x\times \frac{3}{2}\times \frac{5}{3}$$

Multiply \frac{3}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}=\frac{3}{5}x\times \frac{3\times 5}{2\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3}{4}=\frac{3}{5}x\times \frac{5}{2}$$

Multiply \frac{3}{5} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}=\frac{3\times 5}{5\times 2}x$$

Cancel out 5 in both numerator and denominator.

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

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

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

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

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

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$x=\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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