Question

Solve $\frac{1}{5-|x|}\ge 1,x\ne \pm 5$.

Answer 1

Lets assume $x$ is positive, therefore $|x|=x$

$\frac{1}{5-x}\ge 1$

$-x+5\le 1\Rightarrow x\ge 4$

If $x$ is negative, $|x|=-x$

$\frac{1}{5+x}\ge 1$

$x+5\le 1\Rightarrow x\le -4$

Therefore the condition arise that $x=(-\infty ,-4)\cup (4,\infty )$ except for $x=5,-5$