Solve (3/2+7/3:2/3):(2/3+frac{13}{3})=x:(frac{2}{45}*frac{15}{2}+frac{7}{6})

$$( \frac { 3 } { 2 } + \frac { 7 } { 3 } : \frac { 2 } { 3 } ) : ( \frac { 2 } { 3 } + \frac { 13 } { 3 } ) = x : ( \frac { 2 } { 45 } \cdot \frac { 15 } { 2 } + \frac { 7 } { 6 } )$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Divide \frac{7}{3} by \frac{2}{3} by multiplying \frac{7}{3} by the reciprocal of \frac{2}{3}.

$$\frac{\frac{3}{2}+\frac{7}{3}\times \frac{3}{2}}{\frac{2}{3}+\frac{13}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Multiply \frac{7}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{2}+\frac{7\times 3}{3\times 2}}{\frac{2}{3}+\frac{13}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{3}{2}+\frac{7}{2}}{\frac{2}{3}+\frac{13}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Since \frac{3}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+7}{2}}{\frac{2}{3}+\frac{13}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Add 3 and 7 to get 10.

$$\frac{\frac{10}{2}}{\frac{2}{3}+\frac{13}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Divide 10 by 2 to get 5.

$$\frac{5}{\frac{2}{3}+\frac{13}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Since \frac{2}{3} and \frac{13}{3} have the same denominator, add them by adding their numerators.

$$\frac{5}{\frac{2+13}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Add 2 and 13 to get 15.

$$\frac{5}{\frac{15}{3}}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Divide 15 by 3 to get 5.

$$\frac{5}{5}=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Divide 5 by 5 to get 1.

$$1=\frac{x}{\frac{2}{45}\times \frac{15}{2}+\frac{7}{6}}$$

Multiply \frac{2}{45} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$1=\frac{x}{\frac{2\times 15}{45\times 2}+\frac{7}{6}}$$

Cancel out 2 in both numerator and denominator.

$$1=\frac{x}{\frac{15}{45}+\frac{7}{6}}$$

Reduce the fraction \frac{15}{45} to lowest terms by extracting and canceling out 15.

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

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{7}{6} to fractions with denominator 6.

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

Since \frac{2}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 7 to get 9.

$$1=\frac{x}{\frac{9}{6}}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$1=\frac{x}{\frac{3}{2}}$$

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

$$\frac{x}{\frac{3}{2}}=1$$

Multiply both sides by \frac{3}{2}.

$$x=\frac{3}{2}$$