Solve: (2x - 3) / (3x - 5) ≥ 3.
Model Answer & Options
Source: Extra Practicex ∈ (5/3, 12/7]
x ∈ [12/7, ∞)
x ∈ (5/3, ∞)
x ∈ (-∞, 5/3) ∪ [12/7, ∞)
Explanation
Rearrange: (2x - 3) / (3x - 5) - 3 ≥ 0 → [2x - 3 - 3(3x - 5)] / (3x - 5) ≥ 0 → (2x - 3 - 9x + 15) / (3x - 5) ≥ 0 → (-7x + 12) / (3x - 5) ≥ 0. Multiply by -1: (7x - 12) / (3x - 5) ≤ 0. Critical points are 12/7 (≈1.71) and 5/3 (≈1.66). The interval satisfying the 'less than or equal to' sign is between the roots: (5/3, 12/7]. We exclude 5/3 (denominator) and include 12/7.
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