AlgebraVery hardCounting integers satisfying two inequalities
Algebra practice question
How many integers x satisfy both 3 − 2x ≥ x − 9 and x > −1?
Answer: 5
The first gives 12 ≥ 3x, so x ≤ 4. With x > −1, the integers are 0, 1, 2, 3, 4: five of them.
Common wrong answers
- If you answered 3
- 3 misreads x ≤ 4 as x < 4 and drops 0.
- If you answered 4
- 4 leaves out x = 0.
- If you answered 6
- 6 wrongly includes x = −1, but the inequality is strict.
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