How many integers satisfy ?
Answer and explanation
Correct answer: E.
- Step 1: Express the absolute value inequality as a compound inequality: .
- Step 2: Add across the inequality: . Divide by : .
- Step 3: Since , the allowable integer values for run from to , inclusive: . That gives integers.
Answer
.
Why not the others: counts only positive integers (); computes the width of the interval without dividing by ; includes an endpoint beyond ; omits .
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