Solve for x: |3x - 2| ≤ 4.

Model Answer & Options

Source: Extra Practice

[-2/3, 2]

(-2/3, 2)

[2/3, 2]

(-∞, -2/3] ∪ [2, ∞)

Explanation

Correct Option: Using the property |X| ≤ a ⇔ -a ≤ X ≤ a, we get -4 ≤ 3x - 2 ≤ 4. Adding 2 to all parts gives -2 ≤ 3x ≤ 6. Dividing by 3 gives -2/3 ≤ x ≤ 2. In interval notation, this is [-2/3, 2]. Incorrect Options: Option 2 uses open intervals which is incorrect for ≤; Option 3 has an incorrect lower bound; Option 4 represents the solution for |3x - 2| ≥ 4.

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