Solve the inequality (x^2 - 3x - 4) / (x - 5) ≤ 0. Which of the following is the solution set?
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Correct answer
A. (-∞, -1] ∪ [4, 5)
Principle or equation
For a rational inequality, find critical points where numerator or denominator is zero, test intervals, and exclude points where denominator is zero.
Why this answer is correct
Factor numerator: (x-4)(x+1). Critical points: x = -1, 4, 5. Test intervals: (-∞,-1): positive; (-1,4): negative; (4,5): positive; (5,∞): positive. Include -1 and 4 because ≤ 0, exclude 5. Solution: (-∞,-1] ∪ [4,5).
Example
Solve (x-1)/(x-2) ≤ 0: critical 1,2; solution [1,2).
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