What is the solution to (x – 5)(2x + 1)(x – 7) > 0?

The factors are zero at x = −0.5, x = 5, and x = 7, so these values divide the number line into intervals. Testing x = 0 gives (−5)(1)(−7) > 0, so (−0.5, 5) is part of the solution; since the product is positive for x > 7 and negative between 5 and 7, the other solution interval is (7, ∞). The inequality is strict, so the zeros are excluded. Choice A gives (−0.5, 5) ∪ (7, ∞).

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