Solve [5/8div(4/3-1/2)]:x=[(2/3-frac{2}{9})*(1+frac{9}{4})]:[frac{7}{9}div(frac{3}{4}+frac{1}{8})]

$$[ \frac { 5 } { 8 } \div ( \frac { 4 } { 3 } - \frac { 1 } { 2 } ) ] : x = [ ( \frac { 2 } { 3 } - \frac { 2 } { 9 } ) \cdot ( 1 + \frac { 9 } { 4 } ) ] : [ \frac { 7 } { 9 } \div ( \frac { 3 } { 4 } + \frac { 1 } { 8 } ) ]$$

Solve for x

$$x=\frac{6}{13}\approx 0.461538462$$

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.

$$\frac{\frac{5}{8}}{\frac{4}{3}-\frac{1}{2}}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{5}{8}}{\frac{8}{6}-\frac{3}{6}}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{8}}{\frac{8-3}{6}}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{5}{8}}{\frac{5}{6}}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

Divide \frac{5}{8} by \frac{5}{6} by multiplying \frac{5}{8} by the reciprocal of \frac{5}{6}.

$$\frac{5}{8}\times \frac{6}{5}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

Multiply \frac{5}{8} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 6}{8\times 5}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{6}{8}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}=\frac{9}{8}x\left(\frac{2}{3}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

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

$$\frac{3}{4}=\frac{9}{8}x\left(\frac{6}{9}-\frac{2}{9}\right)\left(1+\frac{9}{4}\right)$$

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

$$\frac{3}{4}=\frac{9}{8}x\times \frac{6-2}{9}\left(1+\frac{9}{4}\right)$$

Subtract 2 from 6 to get 4.

$$\frac{3}{4}=\frac{9}{8}x\times \frac{4}{9}\left(1+\frac{9}{4}\right)$$

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

$$\frac{3}{4}=\frac{9\times 4}{8\times 9}x\left(1+\frac{9}{4}\right)$$

Cancel out 9 in both numerator and denominator.

$$\frac{3}{4}=\frac{4}{8}x\left(1+\frac{9}{4}\right)$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{4}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}=\frac{1}{2}x\times \frac{4+9}{4}$$

Add 4 and 9 to get 13.

$$\frac{3}{4}=\frac{1}{2}x\times \frac{13}{4}$$

Multiply \frac{1}{2} times \frac{13}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}=\frac{1\times 13}{2\times 4}x$$

Do the multiplications in the fraction \frac{1\times 13}{2\times 4}.

$$\frac{3}{4}=\frac{13}{8}x$$

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

$$\frac{13}{8}x=\frac{3}{4}$$

Multiply both sides by \frac{8}{13}, the reciprocal of \frac{13}{8}.

$$x=\frac{3}{4}\times \frac{8}{13}$$

Multiply \frac{3}{4} times \frac{8}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\times 8}{4\times 13}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 13}.

$$x=\frac{24}{52}$$

Reduce the fraction \frac{24}{52} to lowest terms by extracting and canceling out 4.

$$x=\frac{6}{13}$$