Is it allowed to solve this inequality $x|x-1|>-3$ by dividing each member with $x$? Is it allowed to solve this inequality  $x|x-1|>-3$ by dividing each member with $x$? What if $x$ is negative?
My textbook provides the following solution:

Divide both sides by $x: $ $\frac { x | x - 1 | } { x } > \frac { - 3
 } { x } ; \quad x \neq 0$
Simplify: $| x - 1 | > - \frac { 3 } { x } ; \quad x \neq 0$

Edit: provided textbook's solution


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