Find the solution set for the absolute value inequality: |2x - 7| <= 9.
Answer and explanation
Correct answer: C. -1 <= x <= 8
- Step 1: Rewrite the absolute value inequality as a compound inequality: -9 <= 2x - 7 <= 9.
- Step 2: Add 7 across all parts: -2 <= 2x <= 16.
- Step 3: Divide by 2: -1 <= x <= 8.
Answer
-1 <= x <= 8.
Why not the others: Option -8 <= x <= 1 swaps signs during isolation. Option 'x <= -1 or x >= 8' solves the inequality for greater than or equal to rather than less than or equal to. Option 1 <= x <= 8 adds 7 incorrectly to -9.
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