AlgebraMediumCounting integers in a compound inequality
Algebra practice question
How many integers x satisfy −3 ≤ 2x + 1 < 9?
Answer: 6
Subtract 1 and halve: −2 ≤ x < 4. The integers are −2, −1, 0, 1, 2, 3 — six of them.
Common wrong answers
- If you answered 5
- Include x = −2: the left side allows equality.
- If you answered 7
- x = 4 is excluded by the strict < on the right; count −2 through 3.
- If you answered 6.0
- Six integers — list them: −2, −1, 0, 1, 2, 3.
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