How do you solve |-4x|/(3-x)<0 ?

Answer 1

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As the LHS side is negative, the numerator and denominator must be of different signs.

There are two scenarios thus:

1) Abs(-4x) is negative, 3-x is postive

2) Abs-4x is positive, 3-x is negative

As the abs function is always positive, then 3-x must always be negative

3-x<0

3<x