Solve (1/5+2/3):2/15=(5/4-x):x

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

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

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.

$$x\times \frac{\frac{1}{5}+\frac{2}{3}}{\frac{2}{15}}=\frac{5}{4}-x$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$x\times \frac{\frac{3}{15}+\frac{10}{15}}{\frac{2}{15}}=\frac{5}{4}-x$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$x\times \frac{\frac{3+10}{15}}{\frac{2}{15}}=\frac{5}{4}-x$$

Add 3 and 10 to get 13.

$$x\times \frac{\frac{13}{15}}{\frac{2}{15}}=\frac{5}{4}-x$$

Divide \frac{13}{15} by \frac{2}{15} by multiplying \frac{13}{15} by the reciprocal of \frac{2}{15}.

$$x\times \frac{13}{15}\times \frac{15}{2}=\frac{5}{4}-x$$

Multiply \frac{13}{15} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$x\times \frac{13\times 15}{15\times 2}=\frac{5}{4}-x$$

Cancel out 15 in both numerator and denominator.

$$x\times \frac{13}{2}=\frac{5}{4}-x$$

Add x to both sides.

$$x\times \frac{13}{2}+x=\frac{5}{4}$$

Combine x\times \frac{13}{2} and x to get \frac{15}{2}x.

$$\frac{15}{2}x=\frac{5}{4}$$

Multiply both sides by \frac{2}{15}, the reciprocal of \frac{15}{2}.

$$x=\frac{5}{4}\times \frac{2}{15}$$

Multiply \frac{5}{4} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 2}{4\times 15}$$

Do the multiplications in the fraction \frac{5\times 2}{4\times 15}.

$$x=\frac{10}{60}$$

Reduce the fraction \frac{10}{60} to lowest terms by extracting and canceling out 10.

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