Answer
$(-1,3/2)$
Work Step by Step
$|1-4x|-7\lt-2$, so $|1-4x|\lt5$ $-5\lt1-4x\lt5$, so $-6\lt-4x\lt4$, so $3/2\gt x\gt-1$, thus the solution set is $(-1,3/2)$
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