What is the solution to 4x 3 – 3x 2 – 7x < 0?

Factor the expression: 4x³ − 3x² − 7x = x(4x² − 3x − 7) = x(x + 1)(4x − 7). Its zeros are −1, 0, and 7/4 (or 1.75). Testing the intervals determined by these zeros shows the expression is negative on (−∞, −1) and (0, 1.75). Because the inequality is strict, the zeros are excluded, so the answer is choice A, (−∞, −1) ∪ (0, 1.75).

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