If the number line is shaded between (-2) and (5), with (-2) closed and (5) open, what is the interval?

Correct answer: ([-2,5))

The direct answer is option C: \([-2,5)\). Interval notation records whether each endpoint is included. A closed dot means the endpoint belongs to the solution, so it uses a square bracket. An open dot means the endpoint is excluded, so it uses a round parenthesis. Here \(-2\) is closed, so the interval starts with \([\). The number 5 is open, so the interval ends with \) . Therefore the interval is \([-2,5)\), meaning \(-2\le x<5\). Option A, \((-2,5)\), excludes both endpoints and therefore wrongly excludes \(-2\). Option B, \([-2,5]\), includes 5 even though its point is open. Option C correctly includes \(-2\) and excludes 5. Option D, \((-2,5]\), does the opposite: it excludes \(-2\) and includes 5. The order of the brackets matters, because it tells exactly what happens at each boundary. Memory cue: square bracket means “included”; round bracket means “not included.”