Solve x:(7/3*21/2-21)=sqrt{(5/3+4/3-frac{2}{6}):(frac{3}{6}+4-frac{1}{3})}:(frac{4}{5}+2)

$$x : ( \frac { 7 } { 3 } \cdot \frac { 21 } { 2 } - 21 ) = \sqrt { ( \frac { 5 } { 3 } + \frac { 4 } { 3 } - \frac { 2 } { 6 } ) : ( \frac { 3 } { 6 } + 4 - \frac { 1 } { 3 } ) } : ( \frac { 4 } { 5 } + 2 )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply \frac{7}{3} times \frac{21}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{7\times 21}{3\times 2}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Do the multiplications in the fraction \frac{7\times 21}{3\times 2}.

$$\frac{x}{\frac{147}{6}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Reduce the fraction \frac{147}{6} to lowest terms by extracting and canceling out 3.

$$\frac{x}{\frac{49}{2}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Convert 21 to fraction \frac{42}{2}.

$$\frac{x}{\frac{49}{2}-\frac{42}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Since \frac{49}{2} and \frac{42}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{49-42}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Subtract 42 from 49 to get 7.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Since \frac{5}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{5+4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Add 5 and 4 to get 9.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Divide 9 by 3 to get 3.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{3-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

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

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{3-\frac{1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9}{3}-\frac{1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9-1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Subtract 1 from 9 to get 8.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

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

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1}{2}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1}{2}+\frac{8}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Since \frac{1}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1+8}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Add 1 and 8 to get 9.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{9}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{27}{6}-\frac{2}{6}}}}{\frac{4}{5}+2}$$

Since \frac{27}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{27-2}{6}}}}{\frac{4}{5}+2}$$

Subtract 2 from 27 to get 25.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{25}{6}}}}{\frac{4}{5}+2}$$

Divide \frac{8}{3} by \frac{25}{6} by multiplying \frac{8}{3} by the reciprocal of \frac{25}{6}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{8}{3}\times \frac{6}{25}}}{\frac{4}{5}+2}$$

Multiply \frac{8}{3} times \frac{6}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{8\times 6}{3\times 25}}}{\frac{4}{5}+2}$$

Do the multiplications in the fraction \frac{8\times 6}{3\times 25}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{48}{75}}}{\frac{4}{5}+2}$$

Reduce the fraction \frac{48}{75} to lowest terms by extracting and canceling out 3.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{16}{25}}}{\frac{4}{5}+2}$$

Rewrite the square root of the division \frac{16}{25} as the division of square roots \frac{\sqrt{16}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4}{5}+2}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4}{5}+\frac{10}{5}}$$

Since \frac{4}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4+10}{5}}$$

Add 4 and 10 to get 14.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{14}{5}}$$

Divide \frac{4}{5} by \frac{14}{5} by multiplying \frac{4}{5} by the reciprocal of \frac{14}{5}.

$$\frac{x}{\frac{7}{2}}=\frac{4}{5}\times \frac{5}{14}$$

Multiply \frac{4}{5} times \frac{5}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{7}{2}}=\frac{4\times 5}{5\times 14}$$

Cancel out 5 in both numerator and denominator.

$$\frac{x}{\frac{7}{2}}=\frac{4}{14}$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$\frac{x}{\frac{7}{2}}=\frac{2}{7}$$

Multiply both sides by \frac{7}{2}.

$$x=\frac{2}{7}\times \frac{7}{2}$$

Cancel out \frac{2}{7} and its reciprocal \frac{7}{2}.

$$x=1$$