Solve (9/2+x):x=[(7/12+5/4-3/2)*frac{10}{3}]:(frac{4}{7}-frac{1}{3}+frac{1}{63})

$$( \frac { 9 } { 2 } + x ) : x = [ ( \frac { 7 } { 12 } + \frac { 5 } { 4 } - \frac { 3 } { 2 } ) \cdot \frac { 10 } { 3 } ] : ( \frac { 4 } { 7 } - \frac { 1 } { 3 } + \frac { 1 } { 63 } )$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

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.

$$\frac{9}{2}+x=\frac{63}{16}x\left(\frac{7}{12}+\frac{5}{4}-\frac{3}{2}\right)\times \frac{10}{3}$$

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{5}{4} to fractions with denominator 12.

$$\frac{9}{2}+x=\frac{63}{16}x\left(\frac{7}{12}+\frac{15}{12}-\frac{3}{2}\right)\times \frac{10}{3}$$

Since \frac{7}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{9}{2}+x=\frac{63}{16}x\left(\frac{7+15}{12}-\frac{3}{2}\right)\times \frac{10}{3}$$

Add 7 and 15 to get 22.

$$\frac{9}{2}+x=\frac{63}{16}x\left(\frac{22}{12}-\frac{3}{2}\right)\times \frac{10}{3}$$

Reduce the fraction \frac{22}{12} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}+x=\frac{63}{16}x\left(\frac{11}{6}-\frac{3}{2}\right)\times \frac{10}{3}$$

Least common multiple of 6 and 2 is 6. Convert \frac{11}{6} and \frac{3}{2} to fractions with denominator 6.

$$\frac{9}{2}+x=\frac{63}{16}x\left(\frac{11}{6}-\frac{9}{6}\right)\times \frac{10}{3}$$

Since \frac{11}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{2}+x=\frac{63}{16}x\times \frac{11-9}{6}\times \frac{10}{3}$$

Subtract 9 from 11 to get 2.

$$\frac{9}{2}+x=\frac{63}{16}x\times \frac{2}{6}\times \frac{10}{3}$$

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

$$\frac{9}{2}+x=\frac{63}{16}x\times \frac{1}{3}\times \frac{10}{3}$$

Multiply \frac{63}{16} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{2}+x=\frac{63\times 1}{16\times 3}x\times \frac{10}{3}$$

Do the multiplications in the fraction \frac{63\times 1}{16\times 3}.

$$\frac{9}{2}+x=\frac{63}{48}x\times \frac{10}{3}$$

Reduce the fraction \frac{63}{48} to lowest terms by extracting and canceling out 3.

$$\frac{9}{2}+x=\frac{21}{16}x\times \frac{10}{3}$$

Multiply \frac{21}{16} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{2}+x=\frac{21\times 10}{16\times 3}x$$

Do the multiplications in the fraction \frac{21\times 10}{16\times 3}.

$$\frac{9}{2}+x=\frac{210}{48}x$$

Reduce the fraction \frac{210}{48} to lowest terms by extracting and canceling out 6.

$$\frac{9}{2}+x=\frac{35}{8}x$$

Subtract \frac{35}{8}x from both sides.

$$\frac{9}{2}+x-\frac{35}{8}x=0$$

Combine x and -\frac{35}{8}x to get -\frac{27}{8}x.

$$\frac{9}{2}-\frac{27}{8}x=0$$

Subtract \frac{9}{2} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{27}{8}x=-\frac{9}{2}$$

Multiply both sides by -\frac{8}{27}, the reciprocal of -\frac{27}{8}.

$$x=-\frac{9}{2}\left(-\frac{8}{27}\right)$$

Multiply -\frac{9}{2} times -\frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\left(-8\right)}{2\times 27}$$

Do the multiplications in the fraction \frac{-9\left(-8\right)}{2\times 27}.

$$x=\frac{72}{54}$$

Reduce the fraction \frac{72}{54} to lowest terms by extracting and canceling out 18.

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