Solve 4/k(1+5/9.8k)=10

$$\frac { 4 } { k } ( 1 + \frac { 5 } { 9.8 } k ) = 10$$

Solve for k

$$k=\frac{98}{195}\approx 0.502564103$$

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 k.

$$4\left(1+\frac{5}{9.8}k\right)=10k$$

Expand \frac{5}{9.8} by multiplying both numerator and the denominator by 10.

$$4\left(1+\frac{50}{98}k\right)=10k$$

Reduce the fraction \frac{50}{98} to lowest terms by extracting and canceling out 2.

$$4\left(1+\frac{25}{49}k\right)=10k$$

Use the distributive property to multiply 4 by 1+\frac{25}{49}k.

$$4+4\times \frac{25}{49}k=10k$$

Express 4\times \frac{25}{49} as a single fraction.

$$4+\frac{4\times 25}{49}k=10k$$

Multiply 4 and 25 to get 100.

$$4+\frac{100}{49}k=10k$$

Subtract 10k from both sides.

$$4+\frac{100}{49}k-10k=0$$

Combine \frac{100}{49}k and -10k to get -\frac{390}{49}k.

$$4-\frac{390}{49}k=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{390}{49}k=-4$$

Multiply both sides by -\frac{49}{390}, the reciprocal of -\frac{390}{49}.

$$k=-4\left(-\frac{49}{390}\right)$$

Express -4\left(-\frac{49}{390}\right) as a single fraction.

$$k=\frac{-4\left(-49\right)}{390}$$

Multiply -4 and -49 to get 196.

$$k=\frac{196}{390}$$

Reduce the fraction \frac{196}{390} to lowest terms by extracting and canceling out 2.

$$k=\frac{98}{195}$$