Question

the number of positive integer solutions of 1/(2x-5) >4/x​

Answer 1

Step-by-step explanation:

We have,

$\frac{1}{2x - 5} > \frac{4}{x}$

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

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

$= > \frac{x - 8x + 20}{x(2x - 5)} > 0$

$= > \frac{ - (7x - 20)}{x(2x - 5)} > 0$

$= > \frac{7x - 20}{x(2x - 5)} < 0$

$= > x < 0 \: \: or \: \: x \in( \frac{5}{2} \: \: to \: \: \frac{20}{7} )$