Solve (5/7-1/49):x=[3/2-(6/25+frac{8}{55})]*(frac{3}{4}+frac{3}{8}-frac{2}{5})

$$( \frac { 5 } { 7 } - \frac { 1 } { 49 } ) : x = [ \frac { 3 } { 2 } - ( \frac { 6 } { 25 } + \frac { 8 } { 55 } ) ] \cdot ( \frac { 3 } { 4 } + \frac { 3 } { 8 } - \frac { 2 } { 5 } )$$

Solve for x

$$x=\frac{748000}{871073}\approx 0.858711038$$

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 2200x, the least common multiple of x,2,25,55,4,8,5.

$$2200\left(\frac{5}{7}-\frac{1}{49}\right)=\left(\frac{3}{2}-\left(\frac{6}{25}+\frac{8}{55}\right)\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Least common multiple of 7 and 49 is 49. Convert \frac{5}{7} and \frac{1}{49} to fractions with denominator 49.

$$2200\left(\frac{35}{49}-\frac{1}{49}\right)=\left(\frac{3}{2}-\left(\frac{6}{25}+\frac{8}{55}\right)\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Since \frac{35}{49} and \frac{1}{49} have the same denominator, subtract them by subtracting their numerators.

$$2200\times \frac{35-1}{49}=\left(\frac{3}{2}-\left(\frac{6}{25}+\frac{8}{55}\right)\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Subtract 1 from 35 to get 34.

$$2200\times \frac{34}{49}=\left(\frac{3}{2}-\left(\frac{6}{25}+\frac{8}{55}\right)\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Express 2200\times \frac{34}{49} as a single fraction.

$$\frac{2200\times 34}{49}=\left(\frac{3}{2}-\left(\frac{6}{25}+\frac{8}{55}\right)\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Multiply 2200 and 34 to get 74800.

$$\frac{74800}{49}=\left(\frac{3}{2}-\left(\frac{6}{25}+\frac{8}{55}\right)\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Least common multiple of 25 and 55 is 275. Convert \frac{6}{25} and \frac{8}{55} to fractions with denominator 275.

$$\frac{74800}{49}=\left(\frac{3}{2}-\left(\frac{66}{275}+\frac{40}{275}\right)\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Since \frac{66}{275} and \frac{40}{275} have the same denominator, add them by adding their numerators.

$$\frac{74800}{49}=\left(\frac{3}{2}-\frac{66+40}{275}\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Add 66 and 40 to get 106.

$$\frac{74800}{49}=\left(\frac{3}{2}-\frac{106}{275}\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Least common multiple of 2 and 275 is 550. Convert \frac{3}{2} and \frac{106}{275} to fractions with denominator 550.

$$\frac{74800}{49}=\left(\frac{825}{550}-\frac{212}{550}\right)\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Since \frac{825}{550} and \frac{212}{550} have the same denominator, subtract them by subtracting their numerators.

$$\frac{74800}{49}=\frac{825-212}{550}\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Subtract 212 from 825 to get 613.

$$\frac{74800}{49}=\frac{613}{550}\left(\frac{3}{4}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{3}{8} to fractions with denominator 8.

$$\frac{74800}{49}=\frac{613}{550}\left(\frac{6}{8}+\frac{3}{8}-\frac{2}{5}\right)\times 2200x$$

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

$$\frac{74800}{49}=\frac{613}{550}\left(\frac{6+3}{8}-\frac{2}{5}\right)\times 2200x$$

Add 6 and 3 to get 9.

$$\frac{74800}{49}=\frac{613}{550}\left(\frac{9}{8}-\frac{2}{5}\right)\times 2200x$$

Least common multiple of 8 and 5 is 40. Convert \frac{9}{8} and \frac{2}{5} to fractions with denominator 40.

$$\frac{74800}{49}=\frac{613}{550}\left(\frac{45}{40}-\frac{16}{40}\right)\times 2200x$$

Since \frac{45}{40} and \frac{16}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{74800}{49}=\frac{613}{550}\times \frac{45-16}{40}\times 2200x$$

Subtract 16 from 45 to get 29.

$$\frac{74800}{49}=\frac{613}{550}\times \frac{29}{40}\times 2200x$$

Multiply \frac{613}{550} times \frac{29}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{74800}{49}=\frac{613\times 29}{550\times 40}\times 2200x$$

Do the multiplications in the fraction \frac{613\times 29}{550\times 40}.

$$\frac{74800}{49}=\frac{17777}{22000}\times 2200x$$

Express \frac{17777}{22000}\times 2200 as a single fraction.

$$\frac{74800}{49}=\frac{17777\times 2200}{22000}x$$

Multiply 17777 and 2200 to get 39109400.

$$\frac{74800}{49}=\frac{39109400}{22000}x$$

Reduce the fraction \frac{39109400}{22000} to lowest terms by extracting and canceling out 2200.

$$\frac{74800}{49}=\frac{17777}{10}x$$

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

$$\frac{17777}{10}x=\frac{74800}{49}$$

Multiply both sides by \frac{10}{17777}, the reciprocal of \frac{17777}{10}.

$$x=\frac{74800}{49}\times \frac{10}{17777}$$

Multiply \frac{74800}{49} times \frac{10}{17777} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{74800\times 10}{49\times 17777}$$

Do the multiplications in the fraction \frac{74800\times 10}{49\times 17777}.

$$x=\frac{748000}{871073}$$