If \(x-2<5\), \(x\in\mathbb{Z}\), and \(x\geq 2\), which are the possible integer values of \(x\)?

Correct answer: \(\{2,3,4,5,6\}\)

Adding 2 to both sides of \(x-2<5\) gives \(x<7\). Since \(x\geq 2\) and \(x\) is an integer, the possible values are the integers from 2 through 6: \(\{2,3,4,5,6\}\). Option B is incorrect because 7 is not allowed by the strict inequality \(x<7\). Exam tip: a strict inequality, such as \(<\) or \(>\), excludes its boundary value.