Solve (7/3+1/5-4/15):x=(3/2+frac{4}{3}):(2-frac{3}{4})

$$( \frac { 7 } { 3 } + \frac { 1 } { 5 } - \frac { 4 } { 15 } ) : x = ( \frac { 3 } { 2 } + \frac { 4 } { 3 } ) : ( 2 - \frac { 3 } { 4 } )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{7}{3}+\frac{1}{5}-\frac{4}{15}=\frac{4}{5}x\left(\frac{3}{2}+\frac{4}{3}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{35}{15}+\frac{3}{15}-\frac{4}{15}=\frac{4}{5}x\left(\frac{3}{2}+\frac{4}{3}\right)$$

Since \frac{35}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{35+3}{15}-\frac{4}{15}=\frac{4}{5}x\left(\frac{3}{2}+\frac{4}{3}\right)$$

Add 35 and 3 to get 38.

$$\frac{38}{15}-\frac{4}{15}=\frac{4}{5}x\left(\frac{3}{2}+\frac{4}{3}\right)$$

Since \frac{38}{15} and \frac{4}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{38-4}{15}=\frac{4}{5}x\left(\frac{3}{2}+\frac{4}{3}\right)$$

Subtract 4 from 38 to get 34.

$$\frac{34}{15}=\frac{4}{5}x\left(\frac{3}{2}+\frac{4}{3}\right)$$

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

$$\frac{34}{15}=\frac{4}{5}x\left(\frac{9}{6}+\frac{8}{6}\right)$$

Since \frac{9}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{34}{15}=\frac{4}{5}x\times \frac{9+8}{6}$$

Add 9 and 8 to get 17.

$$\frac{34}{15}=\frac{4}{5}x\times \frac{17}{6}$$

Multiply \frac{4}{5} times \frac{17}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{34}{15}=\frac{4\times 17}{5\times 6}x$$

Do the multiplications in the fraction \frac{4\times 17}{5\times 6}.

$$\frac{34}{15}=\frac{68}{30}x$$

Reduce the fraction \frac{68}{30} to lowest terms by extracting and canceling out 2.

$$\frac{34}{15}=\frac{34}{15}x$$

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

$$\frac{34}{15}x=\frac{34}{15}$$

Multiply both sides by \frac{15}{34}, the reciprocal of \frac{34}{15}.

$$x=\frac{34}{15}\times \frac{15}{34}$$

Cancel out \frac{34}{15} and its reciprocal \frac{15}{34}.

$$x=1$$