Solve the inequality (x + 3)(2 - x) < 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-∞, -3) ∪ (2, ∞)
Principle or equation
For a product of two factors to be negative, the factors must have opposite signs. The critical points are where each factor is zero: -3 and 2. Test intervals.
Why this answer is correct
Critical points: x = -3 and x = 2. Test x = -4: (-1)(6) = -6 < 0, so (-∞, -3) works. Test x = 0: (3)(2) = 6 > 0, so (-3, 2) does not. Test x = 3: (6)(-1) = -6 < 0, so (2, ∞) works. Since the inequality is strict, endpoints are excluded. Solution: (-∞, -3) ∪ (2, ∞).
Example
Solve (x - 1)(x - 2) < 0. Critical points 1 and 2. Test 0: (+)(-) = - works; test 1.5: (+)(-) = - works; test 3: (+)(+) = + not. Solution (1, 2).
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