Solve (2-9/28:3/7):x=(3/2+7/4-frac{5}{2}):(3-frac{3}{5})

$$( 2 - \frac { 9 } { 28 } : \frac { 3 } { 7 } ) : x = ( \frac { 3 } { 2 } + \frac { 7 } { 4 } - \frac { 5 } { 2 } ) : ( 3 - \frac { 3 } { 5 } )$$

Solve for x

$$x=4$$

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.

$$2-\frac{\frac{9}{28}}{\frac{3}{7}}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

Divide \frac{9}{28} by \frac{3}{7} by multiplying \frac{9}{28} by the reciprocal of \frac{3}{7}.

$$2-\frac{9}{28}\times \frac{7}{3}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

Multiply \frac{9}{28} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$2-\frac{9\times 7}{28\times 3}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{9\times 7}{28\times 3}.

$$2-\frac{63}{84}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

Reduce the fraction \frac{63}{84} to lowest terms by extracting and canceling out 21.

$$2-\frac{3}{4}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

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

$$\frac{8}{4}-\frac{3}{4}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

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

$$\frac{8-3}{4}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

Subtract 3 from 8 to get 5.

$$\frac{5}{4}=\frac{5}{12}x\left(\frac{3}{2}+\frac{7}{4}-\frac{5}{2}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{5}{4}=\frac{5}{12}x\left(\frac{6}{4}+\frac{7}{4}-\frac{5}{2}\right)$$

Since \frac{6}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{5}{4}=\frac{5}{12}x\left(\frac{6+7}{4}-\frac{5}{2}\right)$$

Add 6 and 7 to get 13.

$$\frac{5}{4}=\frac{5}{12}x\left(\frac{13}{4}-\frac{5}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{13}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{5}{4}=\frac{5}{12}x\left(\frac{13}{4}-\frac{10}{4}\right)$$

Since \frac{13}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}=\frac{5}{12}x\times \frac{13-10}{4}$$

Subtract 10 from 13 to get 3.

$$\frac{5}{4}=\frac{5}{12}x\times \frac{3}{4}$$

Multiply \frac{5}{12} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}=\frac{5\times 3}{12\times 4}x$$

Do the multiplications in the fraction \frac{5\times 3}{12\times 4}.

$$\frac{5}{4}=\frac{15}{48}x$$

Reduce the fraction \frac{15}{48} to lowest terms by extracting and canceling out 3.

$$\frac{5}{4}=\frac{5}{16}x$$

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

$$\frac{5}{16}x=\frac{5}{4}$$

Multiply both sides by \frac{16}{5}, the reciprocal of \frac{5}{16}.

$$x=\frac{5}{4}\times \frac{16}{5}$$

Multiply \frac{5}{4} times \frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 16}{4\times 5}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{16}{4}$$

Divide 16 by 4 to get 4.

$$x=4$$