How will the interval ((2,7]) be shown on a number line?

Correct answer: Open circle at (2) closed circle at (7) and shaded between

The direct answer is option A. The interval \((2,7]\) has two different bracket meanings. A round or open bracket at 2 means 2 is excluded, so the graph must have an open circle at 2. A square or closed bracket at 7 means 7 is included, so the graph must have a filled circle at 7. Every real number between them is included, so shade the segment between the two points. Thus the representation is an open circle at 2, a closed circle at 7, and shading between them. Option A matches exactly. Option B reverses both endpoint types. Option C incorrectly excludes 7 as well as 2. Option D incorrectly includes 2 and also includes 7. In inequality form, the same interval is \(2<x\le7\). Remember that a parenthesis means “not included” and a square bracket means “included”; the bracket closest to each number tells its status.