Solve {l}{text{17)}x:(1/6+4/3*1/10)=(1/9*frac{4}{3}:frac{2}{3}):(frac{5}{12}+frac{1}{2}+(frac{1}{2})^3-(1-frac{1}{6}))}

$$\left. \begin{array} { l } { \text { 17) } x : ( \frac { 1 } { 6 } + \frac { 4 } { 3 } \cdot \frac { 1 } { 10 } ) = ( \frac { 1 } { 9 } \cdot \frac { 4 } { 3 } : \frac { 2 } { 3 } ) : ( \frac { 5 } { 12 } + \frac { 1 } { 2 } + ( \frac { 1 } { 2 } ) ^ { 3 } - ( 1 - \frac { 1 } { 6 } ) ) } \end{array} \right.$$

Solve for x

$$x=\frac{8}{25}=0.32$$

Steps for Solving Linear Equation

Multiply \frac{4}{3} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{1}{6}+\frac{4\times 1}{3\times 10}}=\frac{\frac{\frac{1}{9}\times \frac{4}{3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Do the multiplications in the fraction \frac{4\times 1}{3\times 10}.

$$\frac{x}{\frac{1}{6}+\frac{4}{30}}=\frac{\frac{\frac{1}{9}\times \frac{4}{3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{x}{\frac{1}{6}+\frac{2}{15}}=\frac{\frac{\frac{1}{9}\times \frac{4}{3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{2}{15} to fractions with denominator 30.

$$\frac{x}{\frac{5}{30}+\frac{4}{30}}=\frac{\frac{\frac{1}{9}\times \frac{4}{3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Since \frac{5}{30} and \frac{4}{30} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{5+4}{30}}=\frac{\frac{\frac{1}{9}\times \frac{4}{3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Add 5 and 4 to get 9.

$$\frac{x}{\frac{9}{30}}=\frac{\frac{\frac{1}{9}\times \frac{4}{3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{\frac{1}{9}\times \frac{4}{3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Multiply \frac{1}{9} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{\frac{1\times 4}{9\times 3}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Do the multiplications in the fraction \frac{1\times 4}{9\times 3}.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{\frac{4}{27}}{\frac{2}{3}}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Divide \frac{4}{27} by \frac{2}{3} by multiplying \frac{4}{27} by the reciprocal of \frac{2}{3}.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{4}{27}\times \frac{3}{2}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Multiply \frac{4}{27} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{4\times 3}{27\times 2}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Do the multiplications in the fraction \frac{4\times 3}{27\times 2}.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{12}{54}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Reduce the fraction \frac{12}{54} to lowest terms by extracting and canceling out 6.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{5}{12}+\frac{1}{2}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Least common multiple of 12 and 2 is 12. Convert \frac{5}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{5}{12}+\frac{6}{12}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Since \frac{5}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{5+6}{12}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Add 5 and 6 to get 11.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{11}{12}+\left(\frac{1}{2}\right)^{3}-\left(1-\frac{1}{6}\right)}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{11}{12}+\frac{1}{8}-\left(1-\frac{1}{6}\right)}$$

Least common multiple of 12 and 8 is 24. Convert \frac{11}{12} and \frac{1}{8} to fractions with denominator 24.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{22}{24}+\frac{3}{24}-\left(1-\frac{1}{6}\right)}$$

Since \frac{22}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{22+3}{24}-\left(1-\frac{1}{6}\right)}$$

Add 22 and 3 to get 25.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{25}{24}-\left(1-\frac{1}{6}\right)}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{25}{24}-\left(\frac{6}{6}-\frac{1}{6}\right)}$$

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

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{25}{24}-\frac{6-1}{6}}$$

Subtract 1 from 6 to get 5.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{25}{24}-\frac{5}{6}}$$

Least common multiple of 24 and 6 is 24. Convert \frac{25}{24} and \frac{5}{6} to fractions with denominator 24.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{25}{24}-\frac{20}{24}}$$

Since \frac{25}{24} and \frac{20}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{25-20}{24}}$$

Subtract 20 from 25 to get 5.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{2}{9}}{\frac{5}{24}}$$

Divide \frac{2}{9} by \frac{5}{24} by multiplying \frac{2}{9} by the reciprocal of \frac{5}{24}.

$$\frac{x}{\frac{3}{10}}=\frac{2}{9}\times \frac{24}{5}$$

Multiply \frac{2}{9} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{3}{10}}=\frac{2\times 24}{9\times 5}$$

Do the multiplications in the fraction \frac{2\times 24}{9\times 5}.

$$\frac{x}{\frac{3}{10}}=\frac{48}{45}$$

Reduce the fraction \frac{48}{45} to lowest terms by extracting and canceling out 3.

$$\frac{x}{\frac{3}{10}}=\frac{16}{15}$$

Multiply both sides by \frac{3}{10}.

$$x=\frac{16}{15}\times \frac{3}{10}$$

Multiply \frac{16}{15} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{16\times 3}{15\times 10}$$

Do the multiplications in the fraction \frac{16\times 3}{15\times 10}.

$$x=\frac{48}{150}$$

Reduce the fraction \frac{48}{150} to lowest terms by extracting and canceling out 6.

$$x=\frac{8}{25}$$