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