Source: Extra Practice
Solve the inequality |3x - 2| ≥ 7.
Options
Option A is correct
(-∞, -5/3] ∪ [3, ∞)
Option B
[-5/3, 3]
Option C
(-∞, -3] ∪ [5/3, ∞)
Option D
[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.