Solve the inequality |3x - 2| ≥ 7.
Model Answer & Options
Source: Extra Practice(-∞, -5/3] ∪ [3, ∞)
[-5/3, 3]
(-∞, -3] ∪ [5/3, ∞)
[3, ∞)
Explanation
The inequality |a| ≥ b implies a ≥ b or a ≤ -b. For |3x - 2| ≥ 7: Case 1: 3x - 2 ≥ 7 => 3x ≥ 9 => x ≥ 3. Case 2: 3x - 2 ≤ -7 => 3x ≤ -5 => x ≤ -5/3. Combining these gives x ∈ (-∞, -5/3] ∪ [3, ∞). Option B represents |3x - 2| ≤ 7. Option C has the numbers swapped. Option D is incomplete.
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