Find the solution set for the absolute value inequality: |3x - 7| <= 11.
Answer and explanation
Correct answer: A. -4/3 <= x <= 6
- Step 1: Set up the compound inequality: -11 <= 3x - 7 <= 11.
- Step 2: Add 7 to all parts: -4 <= 3x <= 18.
- Step 3: Divide all parts by 3: -4/3 <= x <= 6.
Answer
-4/3 <= x <= 6.
Why not the others: '-6 <= x <= 4/3' inverts the sign boundaries; 'x <= -4/3 or x >= 6' solves |3x - 7| >= 11 (disjunction); 'x <= 6' ignores the lower bound.
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