Solve (1/2-x):x=[2/7*(1-1/5)]:[(1-3/5):(1+frac{2}{5})]

$$( \frac { 1 } { 2 } - x ) : x = [ \frac { 2 } { 7 } \cdot ( 1 - \frac { 1 } { 5 } ) ] : [ ( 1 - \frac { 3 } { 5 } ) : ( 1 + \frac { 2 } { 5 } ) ]$$

Solve for x

$$x=\frac{5}{18}\approx 0.277777778$$

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.

$$\frac{1}{2}-x=\frac{7}{2}x\times \frac{2}{7}\left(1-\frac{1}{5}\right)$$

Cancel out \frac{7}{2} and its reciprocal \frac{2}{7}.

$$\frac{1}{2}-x=x\left(1-\frac{1}{5}\right)$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{1}{2}-x=x\left(\frac{5}{5}-\frac{1}{5}\right)$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-x=x\times \frac{5-1}{5}$$

Subtract 1 from 5 to get 4.

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

Subtract x\times \frac{4}{5} from both sides.

$$\frac{1}{2}-x-x\times \frac{4}{5}=0$$

Combine -x and -x\times \frac{4}{5} to get -\frac{9}{5}x.

$$\frac{1}{2}-\frac{9}{5}x=0$$

Subtract \frac{1}{2} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{9}{5}x=-\frac{1}{2}$$

Multiply both sides by -\frac{5}{9}, the reciprocal of -\frac{9}{5}.

$$x=-\frac{1}{2}\left(-\frac{5}{9}\right)$$

Multiply -\frac{1}{2} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-\left(-5\right)}{2\times 9}$$

Do the multiplications in the fraction \frac{-\left(-5\right)}{2\times 9}.

$$x=\frac{5}{18}$$