Solving the inequality $|-9v| \le 54$

Question

If I have a Problem like $|-9v| \leq 54$, is it okay to break it up like $(-9v) \leq54$ and $-(-9v) \leq54$ and solve? Also, you can just make it positive so that $(9v) \leq54$ and $-(9v)\leq54$ and solve? I just want to know if both ways of thinking are correct.

Thanks

Answer 1

$|x|\le a\iff -a\le x< a$ if real $a\ge0$

$|-x|\le a\iff -a\le -x\le a\iff -a\le x\le a$