Solve (5/4-x):x=21/8:7/4

$$( \frac { 5 } { 4 } - x ) : x = \frac { 21 } { 8 } : \frac { 7 } { 4 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

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.

$$\frac{5}{4}-x=x\times \frac{\frac{21}{8}}{\frac{7}{4}}$$

Divide \frac{21}{8} by \frac{7}{4} by multiplying \frac{21}{8} by the reciprocal of \frac{7}{4}.

$$\frac{5}{4}-x=x\times \frac{21}{8}\times \frac{4}{7}$$

Multiply \frac{21}{8} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}-x=x\times \frac{21\times 4}{8\times 7}$$

Do the multiplications in the fraction \frac{21\times 4}{8\times 7}.

$$\frac{5}{4}-x=x\times \frac{84}{56}$$

Reduce the fraction \frac{84}{56} to lowest terms by extracting and canceling out 28.

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

Subtract x\times \frac{3}{2} from both sides.

$$\frac{5}{4}-x-x\times \frac{3}{2}=0$$

Combine -x and -x\times \frac{3}{2} to get -\frac{5}{2}x.

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

Subtract \frac{5}{4} from both sides. Anything subtracted from zero gives its negation.

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

Multiply both sides by -\frac{2}{5}, the reciprocal of -\frac{5}{2}.

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

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

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

Do the multiplications in the fraction \frac{-5\left(-2\right)}{4\times 5}.

$$x=\frac{10}{20}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

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