Solve 21/5-11/2/2frac{1{2}*x}=3frac{1/2-frac{2}{3}}{2frac{1}{3}+3frac{1}{2}}

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

Solve for x

$$x=\frac{49}{85}\approx 0.576470588$$

Steps for Solving Linear Equation

Multiply 2 and 5 to get 10.

$$\frac{\frac{10+1}{5}-\frac{1\times 2+1}{2}}{\frac{2\times 2+1}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{11}{5}-\frac{1\times 2+1}{2}}{\frac{2\times 2+1}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{11}{5}-\frac{2+1}{2}}{\frac{2\times 2+1}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{11}{5}-\frac{3}{2}}{\frac{2\times 2+1}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Subtract \frac{3}{2} from \frac{11}{5} to get \frac{7}{10}.

$$\frac{\frac{7}{10}}{\frac{2\times 2+1}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{7}{10}}{\frac{4+1}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{7}{10}}{\frac{5}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Express \frac{\frac{7}{10}}{\frac{5}{2}x} as a single fraction.

$$\frac{7}{10\times \frac{5}{2}x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Multiply 10 and \frac{5}{2} to get 25.

$$\frac{7}{25x}=\frac{\frac{3\times 2+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{7}{25x}=\frac{\frac{6+1}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Add 6 and 1 to get 7.

$$\frac{7}{25x}=\frac{\frac{7}{2}-\frac{2}{3}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Subtract \frac{2}{3} from \frac{7}{2} to get \frac{17}{6}.

$$\frac{7}{25x}=\frac{\frac{17}{6}}{\frac{2\times 3+1}{3}+\frac{3\times 2+1}{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{25x}=\frac{\frac{17}{6}}{\frac{6+1}{3}+\frac{3\times 2+1}{2}}$$

Add 6 and 1 to get 7.

$$\frac{7}{25x}=\frac{\frac{17}{6}}{\frac{7}{3}+\frac{3\times 2+1}{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{7}{25x}=\frac{\frac{17}{6}}{\frac{7}{3}+\frac{6+1}{2}}$$

Add 6 and 1 to get 7.

$$\frac{7}{25x}=\frac{\frac{17}{6}}{\frac{7}{3}+\frac{7}{2}}$$

Add \frac{7}{3} and \frac{7}{2} to get \frac{35}{6}.

$$\frac{7}{25x}=\frac{\frac{17}{6}}{\frac{35}{6}}$$

Divide \frac{17}{6} by \frac{35}{6} by multiplying \frac{17}{6} by the reciprocal of \frac{35}{6}.

$$\frac{7}{25x}=\frac{17}{6}\times \frac{6}{35}$$

Multiply \frac{17}{6} and \frac{6}{35} to get \frac{17}{35}.

$$\frac{7}{25x}=\frac{17}{35}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 175x, the least common multiple of 25x,35.

$$7\times 7=85x$$

Multiply 7 and 7 to get 49.

$$49=85x$$

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

$$85x=49$$

Divide both sides by 85.

$$x=\frac{49}{85}$$