Solve x/2frac{1{2}*0,4+22/3:12/3}=1frac{1/3+frac{3}{4}}{2-frac{3}{4}}

$$\frac { x } { 2 \frac { 1 } { 2 } \cdot 0,4 + 2 \frac { 2 } { 3 } : 1 \frac { 2 } { 3 } } = \frac { 1 \frac { 1 } { 3 } + \frac { 3 } { 4 } } { 2 - \frac { 3 } { 4 } }$$

Solve for x

$$x=\frac{13}{3}\approx 4,333333333$$

Steps for Solving Linear Equation

Multiply 2 and 2 to get 4.

$$\frac{x}{\frac{4+1}{2}\times 0,4+\frac{\frac{2\times 3+2}{3}}{\frac{1\times 3+2}{3}}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Add 4 and 1 to get 5.

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

Convert decimal number 0,4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{x}{\frac{5}{2}\times \frac{2}{5}+\frac{\frac{2\times 3+2}{3}}{\frac{1\times 3+2}{3}}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Cancel out \frac{5}{2} and its reciprocal \frac{2}{5}.

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

Divide \frac{2\times 3+2}{3} by \frac{1\times 3+2}{3} by multiplying \frac{2\times 3+2}{3} by the reciprocal of \frac{1\times 3+2}{3}.

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

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{x}{1+\frac{2+6}{2+3}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Add 2 and 6 to get 8.

$$\frac{x}{1+\frac{8}{2+3}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Add 2 and 3 to get 5.

$$\frac{x}{1+\frac{8}{5}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{x}{\frac{5}{5}+\frac{8}{5}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Since \frac{5}{5} and \frac{8}{5} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{5+8}{5}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Add 5 and 8 to get 13.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{1\times 3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Multiply 1 and 3 to get 3.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{3+1}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

Add 3 and 1 to get 4.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{4}{3}+\frac{3}{4}}{2-\frac{3}{4}}$$

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

$$\frac{x}{\frac{13}{5}}=\frac{\frac{16}{12}+\frac{9}{12}}{2-\frac{3}{4}}$$

Since \frac{16}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{16+9}{12}}{2-\frac{3}{4}}$$

Add 16 and 9 to get 25.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{25}{12}}{2-\frac{3}{4}}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{25}{12}}{\frac{8}{4}-\frac{3}{4}}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{25}{12}}{\frac{8-3}{4}}$$

Subtract 3 from 8 to get 5.

$$\frac{x}{\frac{13}{5}}=\frac{\frac{25}{12}}{\frac{5}{4}}$$

Divide \frac{25}{12} by \frac{5}{4} by multiplying \frac{25}{12} by the reciprocal of \frac{5}{4}.

$$\frac{x}{\frac{13}{5}}=\frac{25}{12}\times \frac{4}{5}$$

Multiply \frac{25}{12} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{13}{5}}=\frac{25\times 4}{12\times 5}$$

Do the multiplications in the fraction \frac{25\times 4}{12\times 5}.

$$\frac{x}{\frac{13}{5}}=\frac{100}{60}$$

Reduce the fraction \frac{100}{60} to lowest terms by extracting and canceling out 20.

$$\frac{x}{\frac{13}{5}}=\frac{5}{3}$$

Multiply both sides by \frac{13}{5}.

$$x=\frac{5}{3}\times \frac{13}{5}$$

Multiply \frac{5}{3} times \frac{13}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 13}{3\times 5}$$

Cancel out 5 in both numerator and denominator.

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