#### Answer

All real numbers except $-\frac{7}{8}$.

#### Work Step by Step

We are given:
$|\displaystyle \frac{9-x}{7+8x}|\geq 0$
We can see right away that this equation is almost always true because an absolute value is always positive or 0:
$|x|\geq0$ for all $x$
However, we must make sure the denominator is not 0:
$7+8x\ne 0$
$8x\ne -7$
$x\ne -\frac{7}{8}$
Thus the solution is all real numbers except $-\frac{7}{8}$.