Solve (2/5+1/10):x=(1/6+1/2+frac{2}{9}):(frac{1}{9}+frac{1}{27})

$$( \frac { 2 } { 5 } + \frac { 1 } { 10 } ) : x = ( \frac { 1 } { 6 } + \frac { 1 } { 2 } + \frac { 2 } { 9 } ) : ( \frac { 1 } { 9 } + \frac { 1 } { 27 } )$$

Solve for x

$$x=\frac{1}{12}\approx 0.083333333$$

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.

$$\frac{2}{5}+\frac{1}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{4}{10}+\frac{1}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

Since \frac{4}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{4+1}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

Add 4 and 1 to get 5.

$$\frac{5}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

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

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{1}{6}+\frac{3}{6}+\frac{2}{9}\right)$$

Since \frac{1}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{1+3}{6}+\frac{2}{9}\right)$$

Add 1 and 3 to get 4.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{4}{6}+\frac{2}{9}\right)$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{2}{3}+\frac{2}{9}\right)$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{2}{9} to fractions with denominator 9.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{6}{9}+\frac{2}{9}\right)$$

Since \frac{6}{9} and \frac{2}{9} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}=\frac{27}{4}x\times \frac{6+2}{9}$$

Add 6 and 2 to get 8.

$$\frac{1}{2}=\frac{27}{4}x\times \frac{8}{9}$$

Multiply \frac{27}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}=\frac{27\times 8}{4\times 9}x$$

Do the multiplications in the fraction \frac{27\times 8}{4\times 9}.

$$\frac{1}{2}=\frac{216}{36}x$$

Divide 216 by 36 to get 6.

$$\frac{1}{2}=6x$$

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

$$6x=\frac{1}{2}$$

Divide both sides by 6.

$$x=\frac{\frac{1}{2}}{6}$$

Express \frac{\frac{1}{2}}{6} as a single fraction.

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

Multiply 2 and 6 to get 12.

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