Solve x:(5/4+3/2-5/12)=6/7:(frac{4}{3}+frac{1}{2}-frac{1}{6})

$$x : ( \frac { 5 } { 4 } + \frac { 3 } { 2 } - \frac { 5 } { 12 } ) = \frac { 6 } { 7 } : ( \frac { 4 } { 3 } + \frac { 1 } { 2 } - \frac { 1 } { 6 } )$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

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

Since \frac{5}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

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

Add 5 and 6 to get 11.

$$\frac{x}{\frac{11}{4}-\frac{5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

Least common multiple of 4 and 12 is 12. Convert \frac{11}{4} and \frac{5}{12} to fractions with denominator 12.

$$\frac{x}{\frac{33}{12}-\frac{5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

Since \frac{33}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{33-5}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

Subtract 5 from 33 to get 28.

$$\frac{x}{\frac{28}{12}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

Reduce the fraction \frac{28}{12} to lowest terms by extracting and canceling out 4.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{4}{3}+\frac{1}{2}-\frac{1}{6}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{8}{6}+\frac{3}{6}-\frac{1}{6}}$$

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

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{8+3}{6}-\frac{1}{6}}$$

Add 8 and 3 to get 11.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{11}{6}-\frac{1}{6}}$$

Since \frac{11}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{11-1}{6}}$$

Subtract 1 from 11 to get 10.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{10}{6}}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{x}{\frac{7}{3}}=\frac{\frac{6}{7}}{\frac{5}{3}}$$

Divide \frac{6}{7} by \frac{5}{3} by multiplying \frac{6}{7} by the reciprocal of \frac{5}{3}.

$$\frac{x}{\frac{7}{3}}=\frac{6}{7}\times \frac{3}{5}$$

Multiply \frac{6}{7} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{7}{3}}=\frac{6\times 3}{7\times 5}$$

Do the multiplications in the fraction \frac{6\times 3}{7\times 5}.

$$\frac{x}{\frac{7}{3}}=\frac{18}{35}$$

Multiply both sides by \frac{7}{3}.

$$x=\frac{18}{35}\times \frac{7}{3}$$

Multiply \frac{18}{35} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{18\times 7}{35\times 3}$$

Do the multiplications in the fraction \frac{18\times 7}{35\times 3}.

$$x=\frac{126}{105}$$

Reduce the fraction \frac{126}{105} to lowest terms by extracting and canceling out 21.

$$x=\frac{6}{5}$$