Answer
$-5$
Work Step by Step
We put this word problem into an equation then simplify as follows:
$x-\frac{1}{x}=-\frac{24}{5}$
$x(5x)-\frac{5x}{x}=-\frac{24(5x)}{5}$
$5x^{2}-5=-24x$
$5x^{2}+24x-5=0$
$(5x-1)(x+5)=0$
$5x-1=0$ or $x+5=0$
$5x=1$ or $x=-5$
$x=\frac{1}{5}$ or $x=-5$
We are told that the number is negative, so the only possible answer is $-5$