16Hit1600
AlgebraVery hardSum of integer solutions of an absolute-value inequality

Algebra practice question

What is the sum of all integer values of x that satisfy |x + 3| < 2?

Answer: -9

−2 < x + 3 < 2 gives −5 < x < −1, so the integers are −4, −3, and −2, which sum to −9.

Common wrong answers

If you answered 9
9 has the sign wrong.
If you answered -15
−15 wrongly includes −5 and −1, but the inequality is strict.
If you answered -3
−3 is only the middle value.

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