16Hit1600
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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