Solve 72/3+39/2*0,2/frac{3{5}:0,1+4,2}=2x/frac{7{2}+30,5}

$$\frac { 7 \frac { 2 } { 3 } + \frac { 39 } { 2 } \cdot 0,2 } { \frac { 3 } { 5 } : 0,1 + 4,2 } = \frac { 2 x } { \frac { 7 } { 2 } + 30,5 }$$

Solve for x

$$x=\frac{347}{18}\approx 19,277777778$$

Steps for Solving Linear Equation

Multiply 7 and 3 to get 21.

$$\frac{\frac{21+2}{3}+\frac{39}{2}\times 0,2}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Add 21 and 2 to get 23.

$$\frac{\frac{23}{3}+\frac{39}{2}\times 0,2}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Convert decimal number 0,2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{23}{3}+\frac{39}{2}\times \frac{1}{5}}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Multiply \frac{39}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{23}{3}+\frac{39\times 1}{2\times 5}}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Do the multiplications in the fraction \frac{39\times 1}{2\times 5}.

$$\frac{\frac{23}{3}+\frac{39}{10}}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Least common multiple of 3 and 10 is 30. Convert \frac{23}{3} and \frac{39}{10} to fractions with denominator 30.

$$\frac{\frac{230}{30}+\frac{117}{30}}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Since \frac{230}{30} and \frac{117}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{230+117}{30}}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Add 230 and 117 to get 347.

$$\frac{\frac{347}{30}}{\frac{\frac{3}{5}}{0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Express \frac{\frac{3}{5}}{0,1} as a single fraction.

$$\frac{\frac{347}{30}}{\frac{3}{5\times 0,1}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Multiply 5 and 0,1 to get 0,5.

$$\frac{\frac{347}{30}}{\frac{3}{0,5}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Expand \frac{3}{0,5} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{347}{30}}{\frac{30}{5}+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Divide 30 by 5 to get 6.

$$\frac{\frac{347}{30}}{6+4,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Add 6 and 4,2 to get 10,2.

$$\frac{\frac{347}{30}}{10,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Express \frac{\frac{347}{30}}{10,2} as a single fraction.

$$\frac{347}{30\times 10,2}=\frac{2x}{\frac{7}{2}+30,5}$$

Multiply 30 and 10,2 to get 306.

$$\frac{347}{306}=\frac{2x}{\frac{7}{2}+30,5}$$

Convert decimal number 30,5 to fraction \frac{305}{10}. Reduce the fraction \frac{305}{10} to lowest terms by extracting and canceling out 5.

$$\frac{347}{306}=\frac{2x}{\frac{7}{2}+\frac{61}{2}}$$

Since \frac{7}{2} and \frac{61}{2} have the same denominator, add them by adding their numerators.

$$\frac{347}{306}=\frac{2x}{\frac{7+61}{2}}$$

Add 7 and 61 to get 68.

$$\frac{347}{306}=\frac{2x}{\frac{68}{2}}$$

Divide 68 by 2 to get 34.

$$\frac{347}{306}=\frac{2x}{34}$$

Divide 2x by 34 to get \frac{1}{17}x.

$$\frac{347}{306}=\frac{1}{17}x$$

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

$$\frac{1}{17}x=\frac{347}{306}$$

Multiply both sides by 17, the reciprocal of \frac{1}{17}.

$$x=\frac{347}{306}\times 17$$

Express \frac{347}{306}\times 17 as a single fraction.

$$x=\frac{347\times 17}{306}$$

Multiply 347 and 17 to get 5899.

$$x=\frac{5899}{306}$$

Reduce the fraction \frac{5899}{306} to lowest terms by extracting and canceling out 17.

$$x=\frac{347}{18}$$