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Solve over the real numbers: (3x - 1)/(4x + 1) <= 0.

1. x in (-1/4, 1/3]
2. x in [-1/4, 1/3]
3. x in (-1/3, 1/4]
4. x in (-infinity, -1/4) U [1/3, infinity)

Correct answer: x in (-1/4, 1/3]

Solution

The expression is non-positive between the root of the numerator and the value making the denominator zero. Numerator zero at x = 1/3 is allowed (gives 0). Denominator zero at x = -1/4 is excluded. Sign analysis shows the fraction is negative on (-1/4, 1/3), giving the solution (-1/4, 1/3].

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