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AlgebraMediumCounting integers in a compound inequality

Algebra practice question

How many integers x satisfy −2 < x + 3 ≤ 5?

Answer: 7

Subtracting 3 gives −5 < x ≤ 2, so x can be −4, −3, −2, −1, 0, 1, or 2.

Common wrong answers

If you answered 5
5 counts only −2 through 2, forgetting to subtract 3.
If you answered 6
6 leaves out 2, which the ≤ allows.
If you answered 8
8 includes −5, but the left inequality is strict.

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