Solve the inequality (x - 1)/(x + 2) ≥ 0. What is the solution set?
Show the answer and explanation
Correct answer
A. (-∞, -2) ∪ [1, ∞)
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
Critical points: x = 1 (numerator zero) and x = -2 (denominator zero). Test intervals: (-∞, -2): choose -3, (-3-1)/(-3+2) = (-4)/(-1)=4 >0, so included. (-2,1): choose 0, (-1)/(2) = -0.5 0, included. At x=1, value 0, included. At x=-2, undefined, excluded. So solution is (-∞,-2) ∪ [1,∞).
Example
Solve (x-2)/(x-1) ≥ 0: critical 1,2; test intervals gives (-∞,1) ∪ [2,∞).
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