Answer
$(-\infty,-3/2)\cup(3/2,\infty)$
Work Step by Step
$|-2x|\gt|-3|$, so
$|2x|\gt3$, so
$|x|\gt3/2$, so
$x\gt3/2$ or $x\lt-3/2$, thus the solution set is $(-\infty,-3/2)\cup(3/2,\infty)$
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