Solve the inequality (x - 4)(x + 2) > 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-∞, -2) ∪ (4, ∞)
Principle or equation
For a quadratic inequality of the form (x - a)(x - b) > 0 with a < b, the solution is x < a or x > b, i.e., (-∞, a) ∪ (b, ∞).
Why this answer is correct
Set each factor to zero: x = 4 and x = -2. These are the critical points. Test intervals: For x < -2, both factors are negative, product positive. For -2 < x < 4, first factor negative, second positive, product negative. For x > 4, both positive, product positive. Since the inequality is strict (>), the endpoints are not included. Thus the solution is (-∞, -2) ∪ (4, ∞).
Example
Solve (x - 1)(x + 3) > 0. Critical points: 1 and -3. Test intervals: x < -3 gives positive, -3 < x < 1 gives negative, x > 1 gives positive. Solution: (-∞, -3) ∪ (1, ∞).
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