Solve 937/12-927/3/7,25-2frac{2{3}*2,5}=x/[5frac{2{3}+1,75]:6frac{7}{14}}

$$\frac { 93 \frac { 7 } { 12 } - 92 \frac { 7 } { 3 } } { 7,25 - 2 \frac { 2 } { 3 } \cdot 2,5 } = \frac { x } { [ 5 \frac { 2 } { 3 } + 1,75 ] : 6 \frac { 7 } { 14 } }$$

Solve for x

$$x=-\frac{267}{182}\approx -1,467032967$$

Steps for Solving Linear Equation

Multiply 93 and 12 to get 1116.

$$\frac{\frac{1116+7}{12}-\frac{92\times 3+7}{3}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Add 1116 and 7 to get 1123.

$$\frac{\frac{1123}{12}-\frac{92\times 3+7}{3}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Multiply 92 and 3 to get 276.

$$\frac{\frac{1123}{12}-\frac{276+7}{3}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Add 276 and 7 to get 283.

$$\frac{\frac{1123}{12}-\frac{283}{3}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{1123}{12} and \frac{283}{3} to fractions with denominator 12.

$$\frac{\frac{1123}{12}-\frac{1132}{12}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Since \frac{1123}{12} and \frac{1132}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1123-1132}{12}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Subtract 1132 from 1123 to get -9.

$$\frac{\frac{-9}{12}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Reduce the fraction \frac{-9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{3}{4}}{7,25-\frac{2\times 3+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{3}{4}}{7,25-\frac{6+2}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Add 6 and 2 to get 8.

$$\frac{-\frac{3}{4}}{7,25-\frac{8}{3}\times 2,5}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Convert decimal number 2,5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{3}{4}}{7,25-\frac{8}{3}\times \frac{5}{2}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Multiply \frac{8}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{3}{4}}{7,25-\frac{8\times 5}{3\times 2}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Do the multiplications in the fraction \frac{8\times 5}{3\times 2}.

$$\frac{-\frac{3}{4}}{7,25-\frac{40}{6}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Reduce the fraction \frac{40}{6} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{3}{4}}{7,25-\frac{20}{3}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Convert decimal number 7,25 to fraction \frac{725}{100}. Reduce the fraction \frac{725}{100} to lowest terms by extracting and canceling out 25.

$$\frac{-\frac{3}{4}}{\frac{29}{4}-\frac{20}{3}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{29}{4} and \frac{20}{3} to fractions with denominator 12.

$$\frac{-\frac{3}{4}}{\frac{87}{12}-\frac{80}{12}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Since \frac{87}{12} and \frac{80}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{3}{4}}{\frac{87-80}{12}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Subtract 80 from 87 to get 7.

$$\frac{-\frac{3}{4}}{\frac{7}{12}}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Divide -\frac{3}{4} by \frac{7}{12} by multiplying -\frac{3}{4} by the reciprocal of \frac{7}{12}.

$$-\frac{3}{4}\times \frac{12}{7}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Multiply -\frac{3}{4} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 12}{4\times 7}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Do the multiplications in the fraction \frac{-3\times 12}{4\times 7}.

$$\frac{-36}{28}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Reduce the fraction \frac{-36}{28} to lowest terms by extracting and canceling out 4.

$$-\frac{9}{7}=\frac{x}{\frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}}$$

Divide x by \frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}} by multiplying x by the reciprocal of \frac{\frac{5\times 3+2}{3}+1,75}{\frac{6\times 14+7}{14}}.

$$-\frac{9}{7}=\frac{x\times \frac{6\times 14+7}{14}}{\frac{5\times 3+2}{3}+1,75}$$

Multiply 6 and 14 to get 84.

$$-\frac{9}{7}=\frac{x\times \frac{84+7}{14}}{\frac{5\times 3+2}{3}+1,75}$$

Add 84 and 7 to get 91.

$$-\frac{9}{7}=\frac{x\times \frac{91}{14}}{\frac{5\times 3+2}{3}+1,75}$$

Reduce the fraction \frac{91}{14} to lowest terms by extracting and canceling out 7.

$$-\frac{9}{7}=\frac{x\times \frac{13}{2}}{\frac{5\times 3+2}{3}+1,75}$$

Multiply 5 and 3 to get 15.

$$-\frac{9}{7}=\frac{x\times \frac{13}{2}}{\frac{15+2}{3}+1,75}$$

Add 15 and 2 to get 17.

$$-\frac{9}{7}=\frac{x\times \frac{13}{2}}{\frac{17}{3}+1,75}$$

Convert decimal number 1,75 to fraction \frac{175}{100}. Reduce the fraction \frac{175}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{9}{7}=\frac{x\times \frac{13}{2}}{\frac{17}{3}+\frac{7}{4}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{17}{3} and \frac{7}{4} to fractions with denominator 12.

$$-\frac{9}{7}=\frac{x\times \frac{13}{2}}{\frac{68}{12}+\frac{21}{12}}$$

Since \frac{68}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$-\frac{9}{7}=\frac{x\times \frac{13}{2}}{\frac{68+21}{12}}$$

Add 68 and 21 to get 89.

$$-\frac{9}{7}=\frac{x\times \frac{13}{2}}{\frac{89}{12}}$$

Divide x\times \frac{13}{2} by \frac{89}{12} to get x\times \frac{78}{89}.

$$-\frac{9}{7}=x\times \frac{78}{89}$$

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

$$x\times \frac{78}{89}=-\frac{9}{7}$$

Multiply both sides by \frac{89}{78}, the reciprocal of \frac{78}{89}.

$$x=-\frac{9}{7}\times \frac{89}{78}$$

Multiply -\frac{9}{7} times \frac{89}{78} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\times 89}{7\times 78}$$

Do the multiplications in the fraction \frac{-9\times 89}{7\times 78}.

$$x=\frac{-801}{546}$$

Reduce the fraction \frac{-801}{546} to lowest terms by extracting and canceling out 3.

$$x=-\frac{267}{182}$$