Solve [(3/2+1/4-1/6):(1/5+frac{1}{6})]:(3+frac{14}{27})=(frac{1}{2}+x):x

$$[ ( \frac { 3 } { 2 } + \frac { 1 } { 4 } - \frac { 1 } { 6 } ) : ( \frac { 1 } { 5 } + \frac { 1 } { 6 } ) ] : ( 3 + \frac { 14 } { 27 } ) = ( \frac { 1 } { 2 } + x ) : x$$

Solve for x

$$x = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

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.

$$\frac{27}{95}x\times \frac{\frac{3}{2}+\frac{1}{4}-\frac{1}{6}}{\frac{1}{5}+\frac{1}{6}}=\frac{1}{2}+x$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{27}{95}x\times \frac{\frac{6}{4}+\frac{1}{4}-\frac{1}{6}}{\frac{1}{5}+\frac{1}{6}}=\frac{1}{2}+x$$

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

$$\frac{27}{95}x\times \frac{\frac{6+1}{4}-\frac{1}{6}}{\frac{1}{5}+\frac{1}{6}}=\frac{1}{2}+x$$

Add 6 and 1 to get 7.

$$\frac{27}{95}x\times \frac{\frac{7}{4}-\frac{1}{6}}{\frac{1}{5}+\frac{1}{6}}=\frac{1}{2}+x$$

Least common multiple of 4 and 6 is 12. Convert \frac{7}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{27}{95}x\times \frac{\frac{21}{12}-\frac{2}{12}}{\frac{1}{5}+\frac{1}{6}}=\frac{1}{2}+x$$

Since \frac{21}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27}{95}x\times \frac{\frac{21-2}{12}}{\frac{1}{5}+\frac{1}{6}}=\frac{1}{2}+x$$

Subtract 2 from 21 to get 19.

$$\frac{27}{95}x\times \frac{\frac{19}{12}}{\frac{1}{5}+\frac{1}{6}}=\frac{1}{2}+x$$

Least common multiple of 5 and 6 is 30. Convert \frac{1}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{27}{95}x\times \frac{\frac{19}{12}}{\frac{6}{30}+\frac{5}{30}}=\frac{1}{2}+x$$

Since \frac{6}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{27}{95}x\times \frac{\frac{19}{12}}{\frac{6+5}{30}}=\frac{1}{2}+x$$

Add 6 and 5 to get 11.

$$\frac{27}{95}x\times \frac{\frac{19}{12}}{\frac{11}{30}}=\frac{1}{2}+x$$

Divide \frac{19}{12} by \frac{11}{30} by multiplying \frac{19}{12} by the reciprocal of \frac{11}{30}.

$$\frac{27}{95}x\times \frac{19}{12}\times \frac{30}{11}=\frac{1}{2}+x$$

Multiply \frac{19}{12} times \frac{30}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27}{95}x\times \frac{19\times 30}{12\times 11}=\frac{1}{2}+x$$

Do the multiplications in the fraction \frac{19\times 30}{12\times 11}.

$$\frac{27}{95}x\times \frac{570}{132}=\frac{1}{2}+x$$

Reduce the fraction \frac{570}{132} to lowest terms by extracting and canceling out 6.

$$\frac{27}{95}x\times \frac{95}{22}=\frac{1}{2}+x$$

Multiply \frac{27}{95} times \frac{95}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 95}{95\times 22}x=\frac{1}{2}+x$$

Cancel out 95 in both numerator and denominator.

$$\frac{27}{22}x=\frac{1}{2}+x$$

Subtract x from both sides.

$$\frac{27}{22}x-x=\frac{1}{2}$$

Combine \frac{27}{22}x and -x to get \frac{5}{22}x.

$$\frac{5}{22}x=\frac{1}{2}$$

Multiply both sides by \frac{22}{5}, the reciprocal of \frac{5}{22}.

$$x=\frac{1}{2}\times \frac{22}{5}$$

Multiply \frac{1}{2} times \frac{22}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\times 22}{2\times 5}$$

Do the multiplications in the fraction \frac{1\times 22}{2\times 5}.

$$x=\frac{22}{10}$$

Reduce the fraction \frac{22}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{11}{5}$$