Solve 4/k(1+5/98k)=10

$$\frac { 4 } { k } ( 1 + \frac { 5 } { 98 } k ) = 10$$

Solve for k

$$k=\frac{49}{120}\approx 0.408333333$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 98k, the least common multiple of k,98.

$$98\times 4\left(1+\frac{5}{98}k\right)=980k$$

Multiply 98 and 4 to get 392.

$$392\left(1+\frac{5}{98}k\right)=980k$$

Use the distributive property to multiply 392 by 1+\frac{5}{98}k.

$$392+392\times \frac{5}{98}k=980k$$

Express 392\times \frac{5}{98} as a single fraction.

$$392+\frac{392\times 5}{98}k=980k$$

Multiply 392 and 5 to get 1960.

$$392+\frac{1960}{98}k=980k$$

Divide 1960 by 98 to get 20.

$$392+20k=980k$$

Subtract 980k from both sides.

$$392+20k-980k=0$$

Combine 20k and -980k to get -960k.

$$392-960k=0$$

Subtract 392 from both sides. Anything subtracted from zero gives its negation.

$$-960k=-392$$

Divide both sides by -960.

$$k=\frac{-392}{-960}$$

Reduce the fraction \frac{-392}{-960} to lowest terms by extracting and canceling out -8.

$$k=\frac{49}{120}$$