Solve the rational inequality: (2x - 5)/(x + 3) <= 0.
Answer and explanation
Correct answer: B. -3 < x <= 5/2
- Step 1: Find critical values: numerator is 0 at x = 5/2; denominator is 0 at x = -3. Step 2. The rational expression changes sign at -3 and 5/2. It is negative on (-3, 5/2). Step 3. At x = 5/2, the expression equals 0 (included). At x = -3, denominator is 0 (excluded). Thus -3 < x <= 5/2. Answer: -3 < x <= 5/2. Why not the others: Including -3 makes the denominator zero; the disjoint intervals represent the positive region.
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