Question

The number of solutions of the equation $|x|-9|x|+8=0$ is ___

Answer 1

Answer: 4

$|x{|}^2-9|x|+8=0\Rightarrow |x{|}^2-8|x|-|x|+8=0$
$\Rightarrow (|x|-8)(|x|-1)=0\Rightarrow |x|=8\text{ or }|x|=1$
$x=\pm 8\text{ or }x=\pm 1$
$\therefore \text{ Number of solutions is }4.$